Alligation or Mixture -> Formula/Rule 6

Direct Formula / Rule 6 :
• Theorem: There are 'N' students in a class. Rs X are distributed among them so that each boy gets Rs x and each girl gets Rs y. Then the ratio of boys to the girls is given by

  =	(	X - Ny	)	and
  		Nx - X

  the no. of boys =	(	X - Ny	)	and
  		x - y

  the no. of girls are =	(	Nx - X	)	and
  		x - y
• Example :
There are 65 students in a class, 39 rupees are distributed among them so that each boy gets 80 P and each girl gets 30 P. Find the number of boys and girls in that class.
• Detail Method : 
  Let the ratio of boys to the girls in the

  and the no. of girls =	65 X a
  	a + b

  No. of boys =	65 X b
  	a + b

  or,	65 X a	X 80 +	65 X b	X 30 = 3900
  	a + b		a + b

  or, (5200 - 3900)a = (3900 - 1950)b

  or,	a	=	1950	=	3
  	b		1300		2

  ∴ a : b = 3 : 2

  ∴ the no. of boys =	65 X 3	= 39 and
  	5

  the no. of girls =	65 X 2	= 26
  	5

• Ailigation Method : 
  Here alligation is applicable for "money per boy or girl."

  Mean value of money per student =	3900	= 60 P
  	65

  Boys

  Girls

  80		60		30
  30				20

  ∴ Boys : Girls = 3 : 2
  

  ∴ Number of boys =	65	X 3 = 39
  	3 + 2

  and number of girls = 65 - 39 = 26.
• Quicker Method : Here you can use direct formula : 
  Applying the above theorem, we have
  N = 65 
  X = Rs 39 =3900 P
  x= 80 P 
  y = 30 P

  No. of boys =	3900 - 65 X 30	=	1950	= 39
  	80 - 30		50

  No. of girls =	65 X 80 - 3900	=	1300	= 26
  	80 - 30		50

---

Exercise :
1. There are 60 students in a class, 120 rupees are distributed among them so that each boy gets Rs 2.50 and each girl gets 50 P. Find the ratio of boys to the girls.
2. There are 75 students in a class, 48 rupees are distributed among them so that each boy gets Re 1 and each girl gets 40 P. Find the number of boys and girls in that class.
3. There are 50 students in a class, 32 rupees are distributed among them so that each boy gets Re 1 and each girl gets 50 P. Find the number of girls -and boys in that class. 
Answers : 1 = 3 : 5,   2 = 30, 45,   3 = 36 girls, 14 boys

Alligation or Mixture -> Formula/Rule 5

Direct Formula / Rule 5 :
• Theorem: n gm of sugar solution has x% sugar in it. The quantity of sugar should be added to make it y% in the solution is given by

  = n	(	y - x	)	gm.
  		100 - y

  or Quantity of sugar added

  =	(	Solution (required % value - present % value)	)
  		(100 - required % value)
• Example :
300 gm of sugar solution has 40% sugar in it. How much sugar should be added to make it 50% in the solution?
• Detail Method : 
  300 X 40/100 = 120 gm
  300 - 120 = 180 gm
  180gm = 120 + 60 gm
  so 60 gm 
• Ailigation Method : 
  The existing solution has 40% sugar. And sugar is to be mixed; so the other solution has 100% sugar. So by alligation method:

  40%		50%		100%
  50%				10%

  The two mixtures should be added in the ratio 5 : 1.
  

  Therefore, required sugar =	300	X 1 = 60 gm.
  	5
• Quicker Method : Here you can use direct formula : 

  quantity of sugar added =	300 (50 - 40)	= 60 gm.
  	100 - 50

---

Exercise :
1. A mixture of 40 litres of milk and water contains 10% water. How much water must be added to make 20% water in the new mixture?
2. A petrol pump owner mixed leaded and unleaded petrol in such a way that the mixture contains 10% unleaded petrol. What quantity of leaded petrol should be added to 1 litre mixture so that the percentage of unleaded petrol becomes 5%.
3. 15 litres of a mixture contains 20% alcohol and the rest water. If 3 litres of water be mixed in it, the percentage of alcohol in the new mixture will be: 
Answers : 1 = 5 litres,   2 = 1000 ml,   3 = 16 2/3%

Alligation or Mixture -> Formula/Rule 4

Direct Formula / Rule 4 :
• Theorem: The proportion in which water must be mixed with spirit to gain or to lose x% by selling it at cost price is given by

  =	(	x	)
  		100
• Example :
In what proportion must water be mixed with spirit to gain 16 ²/₃% by selling it at cost price?
• Detail Method : Let the required proportion of water to spirit be a : b and the cost price of spirit be Rs x per litre.
  As per the question,
  Selling price of the mixture = Rs x per litre.
  Cost price of the mixture  

  = x X	100
  	x X 100 100

  = Rs	6x	= per litre.
  	7

  Now, assume that the cost price of water = Rs 0 per litre.

  ∴ (a X 0 + b X x) = (a + b)	6x
  	7

  or, bx = (a + b) =	6	x
  	7

  or, b	(	1 -	6	)	=	6a
  			7			7

  or,	b	=	6a
  	7		7

  or,	a	=	1
  	b		6

  ∴ required ratio = 1: 6 
• Ailigation Method : 
  Let CP of sprit be Re 1 per litre.
  Then SP of 1 litre o f mixture = Rs 1.

  Gain = 16	2	%
  	3

  CP of 1 litre of mixture = Rs	(	100 X 3 X 1	)	= Rs	6
  		350			7

  CP of 1 litre water

  CP of 1 litre pure spirit

  (Rs 0)		Mean price    Rs 6/7		(Rs 1)
  1/7				6/7

  Quantity of water	=	1/7	=	1
  Quantity of spirit		6/7		6

  or Ratio of water and spirit = 1 : 6.
  
• Quicker Method : Here you can use direct formula : 

  the required proportion =	50	= 1 : 6
  	300

---

Exercise :
1. In what proportion must water be mixed with spirit to gain 33 ¹/₃%by selling it at cost price?
2. In what proportion must water be mixed with spirit to gain 16% by selling it at cost price?
3. In what proportion must water be mixed with spirit to gain 25% by selling it at cost price? 
Answers : 1 = 1 : 3,   2 = 4 : 25,   3 = 1 : 4

Alligation or Mixture -> Formula/Rule 3

Direct Formula / Rule 3 : Theorem: A mixture of a certain quantity of milk with 'L' litres of water is worth Rs x per litre. If pure milk be worth Rs y per litre, then the quantity of milk is given by : = L ( x ) litres. y - x Example : A mixture of a certain quantity of milk with 16 litres of water is worth 90 P per litre. If pure milk be worth 108 P per litre how much milk is there in the mixture? Detail Method : Let the quantity of milk be x litres.  (x + 16) 90 = x X 108 + 16 X 0 [because the price of water is 0 P]  Because Selling price of the mixture = 90 per kg given  or, 90x + 16 X 90 = 108x  or, 18x = 16 X 90  or, x = 80 litres.  ∴ The quantity of milk = 80 litres. Ailigation Method :  The mean value is 90 P and the price of water is 0 P. milk water 108 Mean price      90 0 90 - 0 108 - 90 = 90 : 18 By the Alligation Rule, milk and water are in the ratio of 5 : 1. ∴ quantity of milk in the mixture = 5 X 16= 80 litres. Quicker Method : Here you can use direct formula :  Quantity of milk in the mixture = 16 ( 90 )  = 16 X 5 = 80 litres. 108 - 90 Exercise : A mixture of a certain quantity of milk with 25 litres of water is worth Rs 2 per litre. If pure milk be worth Rs 12 per litre how much milk is there in the mixture? A mixture of a certain quantity of milk with 16 litres of water is worth Rs 3 per litre. If pure milk be worth Rs 7 per litre how much milk is there in the mixture? A mixture of a certain quantity of milk with 32 litres of water is worth Rs 1.50 per litre. If pure milk be worth Rs 4.50 per litre how much milk is there in the mixture?  Answers : 1 = 5 litres,   2 = 12 litres,   3 = 16 litres

Alligation or Mixture -> Formula/Rule 2

Direct Formula / Rule 2 :
• Theorem: The quantity of salt at Rs x per kg that a man must mix with n kg of salt at Rs y per kg, so that he may, on selling the mixture at Rs z per kg, gain p% on the outlay is given by
  = [ ^{100z - y(100 + p)}/_{x(100 + p) - 100z} ] X n
  
  Note : if we suppose that the quantity of salt at Rs x be m, then we have.
• Example :
How many kg of salt at 42 P per kg must a man mix with 25 kg of salt at 24 P per kg, so that he may, on selling the mixture at 40 per kg, gain 25% on the outlay?
• Detail Method : Let the required amount of salt be x kg
   As per Question,
   Because Selling price of the mixture = 40 per kg given
   so Cost price,of the mixture = 40 X ¹⁰⁰/₁₂₅ X (x + 25)
   or, 42x + 24 x 25 = 32x + 32 x 25
   or, 10x = 25 x 8 
   so x = 20 kg.
• Ailigation Method : 
  Cost price,of the mixture = 40 + ¹⁰⁰/₁₂₅ P = 32 p per kg..
  By the rule of fraction :

  42		Mean price      32		24
  8				10

  Ratio = 4 : 5
  Thus for every 5 kg of salt at 24 P, 4 kg of salt at 42 P is used.
  the required no. of kg = 25 x ⁴/₅ = 20
  
• Quicker Method : Here you can use direct formula : 
  = [ ^{100z - y(100 + p)}/_{x(100 + p) - 100z} ] X n
  = [ ^{100 x 40 - 24(100 + 25)}/_{42 x (100 + 25) - 100 x 40} ] X 25
  = [ ^{4000 - 3000}/_{5250 - 4000} ] X 25
  = [ ¹⁰⁰⁰/₁₂₅₀ ] X 25 = 20 kg.

---

Exercise :
1. Jaydeep purchased 25 kg of rice at the rate of Rs 16.50 per kg and 35 kg ofrice at the rate of Rs 25.50 per kg. He mixed the two and sold the mixture. Approximately, at What price per kg did he sell the mixture to make 25 per cent profit?   [Hint : here you need to find z as per formula]
2. Jagtar purchases 30 kg of wheat at the rate of Rs 11.50 per kg and 20 kg ofwheat at the rate of Rs 14.25 per kg. He mixed the two and sold the mixture. Approximately at what price per kg should he sell the mixture to make 30 per cent profit?   [Hint : here you need to find z as per formula]
3. In what proportion must a grocer mix one kind of wheat at Rs 4.50 per kg with another at Rs 4 per kg in order that by selling the mixture at Rs 5.20 per kg he may make a profit of 20 per cent?
Answers : 1 = Rs 26.50,   2 = Rs 16.30,   3 = 2 : 1

Alligation or Mixture -> Formula/Rule 1

Direct Formula / Rule 1 :
• Theorem: The proportion in which sugar at Rs. x per kg must be mixed with rice at Rs. y per kg, so that the mixture be worth Rs. z a kg, is given by

  =	(	y - z	)
  		z - x

• Example :
The proportion in which sugar at Rs. 3.10 per kg must be mixed with sugar at Rs. 3.60 per kg, so that the mixture be worth Rs. 3.25 a kg ?
• Detail Method : Let the required ratio be x. y.
   As per Question,
   310x + 360y = 325(x+y)
   or 310x + 360y = 325x + 325y
   325x - 310x = 360y - 325y
   150x = 350y
   15x = 35y
   3x = 7y

  =	x	:	7
  	y		3

   so x : y = 7 : 3    [here y goes to left side & 3 goes to right side]
• Ailigation Method : By the rule of alligation we have :

  C.P.of 1 kg cheaper sugar

  C.P.of 1 kg dearer sugar

  (310 paise)		Mean price (325 paise)		(360 paise)
  35				15

  So, ratio of 1st and 2nd quantities = 35 : 15 = 7 : 3 
  so, they must be mixed in the ratio of = 7 : 3
• Quicker Method : Here you can use direct formula : 

  =	(	y - z	)
  		z - x

  =	(	CP of dearer - Mean Price	)
  		Mean Price - CP of cheaper

  =	(	3.60 - 3.25	)	=	(	0.35	)
  		3.25 - 3.10				0.15

  so, they must be mixed in the ratio of = 7 : 3

---

Exercise :
1. In what proportion must rice at Rs 21 per kg be mixed with rice at Rs 28 per kg, so.that the mixture be worth Rs. 25 a kg ? 
2. In what ratio, must coffee at Rs. 62 per kg Is mixed With coffee at Rs. 72 per kg so that the mixture must be worth RS. 64.50 per kg ? 
3. In what ratio must water be mixed with oil costing Rs. 12 per litre to obtain a mixture worth of Rs. 8 per litre ? 
Answers :
1 = 5 : 4,   2 = 3 : 1,   3 = 1 : 2

• #DipaKarmakar clinches gold medal in vault event of FIG Artistic #Gymnastics World Challenge Cup in #Turkey.

• #South Korean President Moon Jae-in arrives in Delhi on four day visit to India.

• HRD Minister @PrakashJavdekar to inaugurate 17th #WorldSanskritConference in Vancouver, #Canada tomorrow.

• India becomes 69th shareholder of the European Bank for Reconstruction andDevelopment, paving way for more joint investment with Indian companies.

• भारत यूरोपीय पुनर्निर्माण और विकास बैंक का 69वां शेयरधारक बना। भारतीय कंपनियों के साथ और अधिक संयुक्‍त निवेश का रास्‍ता साफ।

25 JUNE 2018

• Prime Minister Narendra Modi says India and Seychelles are committed to maintaining peace and stability in Indian Ocean region; both countries sign six agreements for cooperation in various fields including education and cyber security.

• प्रधानमंत्री नरेन्द्र मोदी ने कहा - भारत और सेशल्स हिंद महासागर क्षेत्र में शांति और स्थिरता बनाए रखने के लिए प्रतिबद्ध। दोनों देशों के बीच शिक्षा और साइबर सुरक्षा सहित कई क्षेत्रों में सहयोग के 6 समझौतों पर हस्ताक्षर किये गये।
• On 43rd anniversary of Emergency today, Prime Minister describes it as a direct attack on Constitutional ideals.
• Monsoon Session of Parliament to begin from 18th of next month.
• Vice President M Venkaiah Naidu says, cooperatives have the potential to revive agriculture and make it sustainable.
• Delhi High Court stays felling of trees in the national capital till 4th July.
• Monsoon arrives in Gujarat and Bihar.
• And in FIFA World Cup, final round of group matches begins;  In Pool-A, Uruguay face Russia while Egypt take on Saudi Arabia; In Pool-B, Portugal to clash with Iran while Spain to meet Morocco.
• आपातकाल की 43वीं वर्षगांठ पर आज प्रधानमंत्री ने कहा - यह संवैधानिक आदर्शो पर हमला था।
• संसद का मॉनसून सत्र अगले महीने की 18 तारीख से शुरू।
• उप-राष्ट्रपति एम. वेंकैया नायडू ने कहा - सहकारी संस्थाएं खेती में फिर से जान डालने में सक्षम हैं।
• दिल्‍ली उच्‍च न्‍यायालय ने राजधानी में पेड़ काटने पर चार जुलाई तक रोक लगाई।
• मानसून गुजरात और बिहार में पहुंचा।
• फीफा विश्‍व कप में फाइनल राउंड के ग्रुप मैच शुरू। पूल-ए में उरूग्‍वे का मुकाबला रूस से जबकि सऊदी अरब का सामना मिस्र से। पूल-बी में ईरान का मैच पुर्तगाल से, जबकि स्‍पेन और मोरक्‍को आमने-सामने होंगे।

26 JUNE 2018

• प्रधानमंत्री नरेन्‍द्र मोदी ने कहा-समूचे विश्‍व का भारतीय अर्थव्‍यवस्‍था में विश्‍वास बढ़ रहा है।
• सेशल्‍स के राष्‍ट्रपति ने कहा-उनका देश भारत का समर्पित मित्र और सहयोगी बना रहेगा।
• सरकार ने दोहराया है कि वह अनुसूचित जाति और जनजाति अत्‍याचार निवारण अधिनियम को उसके वास्‍तविक स्‍वरूप में बनाये रखने के लिए प्रतिबद्ध।
• भारतीय जनता पार्टी आपातकाल की 43वीं वर्षगांठ पर काला दिवस मना रही है। प्रधानमंत्री ने जोर देकर कहा-इसका उद्देश्‍य आपातकाल के खतरों के बारे में जागरूकता पैदा करना है।
• राष्‍ट्रपति रामनाथ कोविंद ने कहा कि राष्‍ट्रीय सुरक्षा और विकास तथा जन कल्‍याण के लक्ष्‍य को हासिल करने के समक्ष नशे की लत एक चुनौती।
• फीफा विश्‍वकप में अन्तिम 16 की दो टीमों के लिए मुकाबले आज। ग्रुप सी में ऑस्‍ट्रेलिया और पेरू तथा डेनमार्क तथा फ्रांस का मुकाबला जारी। ग्रुप डी में देर रात नाइजीरिया और अर्जेंटीना तथा आइसलैंड और क्रोएशिया का मुकाबला होगा।
• Prime Minister Narendra Modi says, global confidence in India’s economy is rising.
• Seychelles President says, his country will always be a faithful friend and partner to India.
• Government reiterates its commitment to maintain SC & ST Prevention of Atrocities Act in its original form.
• BJP observes Black Day to mark 43rd anniversary of Emergency; Prime minister stresses on the observance to create awareness about its perils.
• President Ram Nath Kovind says, drug addiction poses a challenge to national security as well as development and public welfare goals.
• Britain's Queen Elizabeth grants royal assent to Prime Minister Theresa May's flagship Brexit legislation.
• And in the FIFA World Cup, two round of sixteen berths at stake today; Nigeria face Argentina while Iceland meet Croatia in Group-D; Australia face Peru, Denmark meet France in Pool-C.

27 JUNE 2018

• US Supreme Court upholds Trump administration's travel ban on people from five Muslim-majority countries.

• अमरीका की सुप्रीम कोर्ट ने मुस्लिम बहुल पांच देशों के नागरिकों पर ट्रंप प्रशासन का यात्रा प्रतिबंध जारी रखा।

The US Supreme Court has ruled in favour of the Trump administration's travel ban targeting people from several Muslim-majority countries. Lower courts had deemed the ban unconstitutional, but the US top court last night reversed the decision in a 5-4 majority ruling. The ban prohibits most people from Iran, Libya, Somalia, Syria and Yemen from entering the United States. President Trump has welcomed the decision. In a tweet, he said, the ruling is a tremendous victory for the American People and the US Constitution.

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China will cut import tariffs on soybean and some other goods from India and four other Asian nations from 1st of July 1. China's Cabinet announced the decision yesterday, amidst a looming trade war with the US. China will reduce tariffs on soybean imported from India, South Korea, Bangladesh, Laos, and Sri Lanka from the current three per cent to zero.

• In FIFA world cup; Argentina and Denmark book their berths for the knockout round.

• और फीफा विश्वकप में अर्जेंटीना और डेनमार्क ने नॉकआऊट राउंड में जगह बनाई। 

"In the ongoing FIFA World Cup, Argentina and Denmark have become the latest teams to qualify for the knockout round. In matches played last night, Argentina beat Nigeria 2-1, while Denmark played a goalless draw with already qualified France to finish second in their group. Most eyes were on Argentina in their do-or-die Group D match with Nigeria in Saint Petersburg. Lionel Messi's World Cup dream was hanging by a thread before yesterday's crucial fixture.  The 31-year old Barcelona forward did his work in the 14th minute, to give Argentina a deserved 1-nil half-time lead.  After Nigeria equalised through a Victor Moses penalty in the 51st minute. Argentina's match-winner came through Marcos Rojo in the 86th minute.

Argentina will now take on France on Saturday in Kazan in the second round. In the Group C game in Moscow, France secured first place ahead of Denmark following a goalless draw. Denmark confirmed their berth in the knockout round with five points, while top-placed France had 7 points. Denmark will face Croatia in Round Sixteen on Sunday. In today's four fixtures, Mexico face Sweden, South Korea play against Germany, Serbia meet Brazil while Switzerland are pitted against(fight against) Costa Rica. 

The world's largest multilateral naval exercise Rim of the Pacific (RIMPAC) will begin today off Hawaii in the Western Pacific Ocean. The two-month long biennial exercise is likely to be attended by navies of 26 countries including India. The Navy in a statement said, INS Sahyadri has already reached the Pearl Harbour in Hawaii to participate in the 26th edition of RIMPAC exercise.

दुनिया का सबसे बड़ा बहुराष्‍ट्रीय नौसैनिक अभ्‍यास रिम ऑफ द पैसिफिक-रिमपैक आज पश्चिमी प्रशांत महासागर में हवाई के पास शुरू होगा। हर दो वर्ष में होने वाले दो महीने के इस नौसैनिक अभ्‍यास में भारत समेत 26 देशों की नौसेना के शामिल होने की आशा है। भारतीय नौसैनिक पोत सहयाद्री 26वें रिमपैक अभ्‍यास में भाग लेने के लिए हवाई में पर्ल हार्बर पहुंच चुका है। आईएनएस सहयाद्री अत्‍याधुनिक तकनीक से बना स्‍वदेशी पोत है।

24 JUNE 2018

• Mr Modi to inaugurate Mundka-Bahadurgarh corridor of the Delhi Metro today.

• श्री नरेन्द्र मोदी आज दिल्ली मैट्रो के मुंडका-बहादुरगढ़ सेक्शन का उद्धघाटन करेंगे।

Prime Minister Narendra Modi will inaugurate the 11.2  kilometre long fully-elevated Mundka-Bahadurgarh corridor of  Delhi Metro's Green Line today. He will inaugurate the facility through  Video Conferencing.  Union Urban Affairs Minister Hardeep Puri and Haryana Chief Minister Manohar Lal Khattar will attend the function in Bahadurgarh.

The Mundka - Bahadurgarh stretch, with seven stations, will be an extension of the existing Green Line from Inderlok to Mundka.  This section will be metro's third line of connectivity to the neighbouring state of Haryana. Metro services are already operational in Gurgram and Faridabad. The services on the new corridor will begin from 4 PM for the public. After the opening of this corridor, the entire Inderlok-Bahadurgarh section will become 26.33 km long and the Delhi Metro network will expand to 288 km with 208 stations.

• In Maharashtra, legal heir or wife of martyred soldier to get two hectares land.

• महाराष्ट्र सरकार शहीद सैनिकों की पत्नियों या उनके कानूनी उत्तराधिकारियों को दो हेक्टेयर कृषि भूमि देगी।

Capital: MumbaiGovernor: C. Vidyasagar RaoChief minister: Devendra Fadnavis

Maharashtra Chief Minister Devendra Fadnavis has announced that the state will give a compensation of two hectares of agricultural land to the legal heir of martyred soldiers, in case their spouses are not alive.

"On March 20 this year, the Maharashtra government had decided to give two hectares of land to the wives of martyred soldiers. A statement from the Chief Minister's office has said that legal heir has also been included in the list and in case the spouse of the martyred soldier is not alive, the land could be given to the legal heir of the soldier. The changes, required in land allotment rules to implement this decision, were approved by Mr Fadnavis yesterday. The decision would apply to the Army as well as the other armed forces of the Union.

• Turkey to hold first simultaneous Presidential and Parliamentary elections today.

• तुर्की में आज पहली बार राष्ट्रपति और संसदीय चुनाव एक साथ।

Turkey holds its first simultaneous Presidential and Parliamentary elections today. This is in line with last year's constitutional changes that will transform the country's Parliamentary system to an executive Presidential one. President Tayyip Erdogan faces his biggest electoral challenge, from former teacher Muharrem Ince, who has revitalised the opposition in less than two months.

Mr Erdogan, 64 called early polls as they were originally set for November 2019. Fifty-four-old Mr Ince, a former physics teacher from northwest Turkey, is an outspoken lawmaker of the secularist Republican People's Party. Voting at diplomatic missions outside the country ended on June 19th. The elections are taking place under a state of emergency, in place since July 2016 following a failed deadly coup blamed by the government on the movement of Fethullah Gulen, a US-based self-exiled religious leader.

• Zimbabwe President survives bomb attack at an election rally in Bulawayo.

• जिम्बाब्वे के राष्ट्रपति बुलावायो में चुनाव रैली में हुए बम हमले में बाल-बाल बचे।

Zimbabwe's President Emmerson Mnangagwa has survived an apparent bomb attack at an election rally of the ruling party in Bulawayo. He said an object exploded yesterday a few inches away from him, but it was not his time. State broadcaster  ZBC reported that 42 people were injured, six of them seriously. The seventy-five year old President visited the injured in hospital. He condemned the violence as senseless and pleaded for unity.

Mr Mnangagwa was in Bulawayo, Zimbabwe's second largest city and also an opposition stronghold, to campaign for his Zanu-PF party ahead of nationwide elections on the 30th of July. He took power in November 2017 after longtime leader Robert Mugabe stepped down following a military intervention.

• In FIFA, Germany come back from brink to beat Sweden 2-1.

• फीफा फुटबॉल विश्वकप में स्वीडन को 2-1 से हराकर जर्मनी अंतिम 16 की दौड़ में बरकरार। 

 FIFA World Cup:

"Defending champions Germany avoided a humiliating exit from the tournament last night, as they came back from behind to beat Sweden, 2-1 in a thrilling Group-F match to revive their hopes of securing a place in the knock-out stage. Marco Reus gave Germany a lifeline in the second half when he cancelled out Ola Toivonen's 32nd minute strike. The holders were hanging by the thread when Jerome Boateng was sent off, but Toni Kroos hit a free-kick in the final minute of injury-time giving Germany hopes of becoming the first side to retain the World Cup since 1962.

In the other Pool-F game, Mexico defeated South Korea, 2-1 to strengthen their chances of sealing a place in the Round-of-16. In Group-G, Belgium crushed Tunisia, 5-2 to all but book a place in the pre-quarterfinals. Romelu Lukaku, who netted a brace along with Eden Hazard, joined Cristiano Ronaldo as the leading goal scorer of the tournament with 4 goals, and also became Belgium's all-time top scorer in major tournaments. Today, England will face Panama in Pool-G, with Japan battling it out against Senegal, and Poland playing Colombia in Group-H.

Headquarters: Vienna, Austria
Founded: September 1960, Baghdad, Iraq

The Organization of the Petroleum Exporting Countries, OPEC and non-OPEC oil producers have agreed to jointly increase the oil production. The meeting in Vienna between OPEC and non-OPEC oil producers including Russia yesterday decided to stick to 100 per cent conformity of the oil production cap set in the meeting in 2016 in which the agreement to cut oil output by a total of 1.8 million barrels per day had been reached. The agreement would be implemented in July.

तीन दिन का वार्षिक सिंधु दर्शन उत्सव आज से जम्मू-कश्मीर के लद्दाख क्षेत्र में सिंधु नदी के तट पर आरंभ हो रहा है। सिंधु दर्शन यात्रा समिति और लद्दाख फांदे सोग्सपा, लेह द्वारा आयोजित उत्सव का उद्घाटन राष्ट्रीय स्वयंसेवक संघ के महासचिव भैय्या जी जोशी करेंगे।

यह 22वां सिंधु दर्शन उत्सव है। इसकी शुरुआत 1997 में तत्कालीन उप प्रधानमंत्री लाल कृष्ण आडवाणी ने की थी।