Alligation or Mixture - Aptitude Questions and Answers - in Hindi

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In what ratio should water be mixed with wine that costs Rs. 60 per litre so that after selling the resultant mixture at Rs.50 per litre, the profit will be 25%?


किस अनुपात मे पानी को 60 रुपये  प्रति लीटर की शराब के साथ मिलाया जाय ताकि मिश्रण को 50 रुपये  प्रति लीटर मे बेचने पर 25 प्रतिशत का लाभ हो?

A)
1 : 2

B)
2 : 3

C)
3 : 4

D)
4 : 5


Correct Answer :

1: 2


Explanation :

Let X is the cost of pure wine. Then,
Cost of resultant mixture, X + 25% of X = 50
100X + 25X = 50*100
125X = 50 *100
X = 5000/125 = Rs. 40

So, wine of Rs. 40(CP) sold at Rs. 50(SP)

Now, in Rs. 60 = 1 litre wine.
So, in Rs.40 = 40/60 = 2/3 part wine, remaining part 1/3 water.
Therefore ratio Water : Wine = 1/3 : 2/3
= 1:2

In what ratio should water be mixed with wine, that costs Rs.60 per litre, so that the price of the resultant mixture is Rs.40 per litre?


किस अनुपात में पानी को 60 रू प्रति लीटर की शराब के साथ मिलाया जाए ताकि मिश्रण का मूल्य 40 रू प्रति लीटर हो जाए?

A)
2 : 3

B)
4 : 5

C)
3 : 4

D)
1 : 2


Correct Answer :

1 : 2


Explanation :

By the rule of alligation: If two ingredients are mixed, then
Quantity of cheaper/Quantity of dearer =[(C.P. of dearer) - (Mean price)] / (Mean price) - [(C.P. of cheaper)]

i.e. (Cheaper Quantity):(Dearer quantity)= (d-m):(m-c).

C.P. of cheaper(in paise) ,Water c=0/lit
C.P. of dearer(in paise),Wine d=60/lit
Mean price(in paise) or resultant mixture costs, m= 40/lit

Thus ,(Cheaper Quantity):(Dearer quantity)= (60-40) / (40- 0)
=> 20:40 =>1:2

16 litres of kerosene is mixed with 5 litres of petrol. The price of kerosene is Rs. 12 per litre and price of petrol is Rs. 33 per litre. The average price of the resultant mixture per litre is?


16 लीटर केरोसीन को 5 लीटर पेट्रोल के साथ मिलाया गया। केरोसीन का मूल्य 12 रू प्रति लीटर और पेट्रोल का मूल्य 33 रू प्रति लीटर है। मिश्रण का औसत मूल्य प्रति लीटर होगा?

A)
15 rs

B)
17 rs

C)
21 rs

D)
23 rs


Correct Answer :

17 rs


Explanation :

Average price of the resultant mixture= (16×12+5×33) / (16+5)
=357 / 21
=17

There is 10% water in 100 liters mixture of milk and water. How much more water is to be added to the mixture so that the resultant solution contains 25% water?


100 लीटर दूध और पानी के मिश्रण में 10 प्रतिशत पानी है। कितना पानी ओर मिला दिया जाये जिससे उसका प्रतिशत मिश्रण का 25 प्रतिशत हो जाए?

A)
15 litre
/
15 लीटर

B)
20 litre
/
20 लीटर

C)
10 litre
/
10 लीटर

D)
None of these
/
इनमे से कोई नही


Correct Answer :

20 litre

/

20 लीटर


Explanation :

There is 10% water in 100 liters mixture of milk and water. How much more water is to be added to the mixture so that the resultant solution contains 25% water?

Initial Solution = 100
Initial water =10% of 100 = 10

Let x is the water to be added to the mixture so that the new mixture must have 25% water

new Solution = 100+x
water in new Solution = 10+x

10+x = 25% of (100+x)
10+x = (25/100)*(100+x)
10+x = (1/4)*(100+x)
40+4x=100+x
3x = 60
x = 20 L

In what ratio should the wheat that costs Rs.7.50 per kg, be mixed with the wheat that costs Rs.11 per kg so that the resultant mixture costs Rs.8.25 per kg?


7.50 रू प्रति किलो गेहूँ को 11 रू प्रति किलो गेहूँ के साथ किस अनुपात में मिलाया जाय ताकि मिश्रण का मूल्य 8.25 रू प्रति किलो है?

A)
8 : 5

B)
9 : 7

C)
11 : 3

D)
10 : 3


Correct Answer :

11 : 3


Explanation :

By the rule of alligation: If two ingredients are mixed, then
Quantity of cheaper/Quantity of dearer =[(C.P. of dearer) - (Mean price)] / (Mean price) - [(C.P. of cheaper)]

i.e. (Cheaper Quantity):(Dearer quantity)= (d-m):(m-c).

C.P. of cheaper(in paise) , c=750
C.P. of dearer(in paise), d=1100
Mean price(in paise) or resultant mixture costs, m= 825

Thus ,(Cheaper Quantity):(Dearer quantity)= (1100-825) / (825- 750)
= (1100-825) / (825- 750)
=275 / 75
=11 / 3

How much water is to be mixed in 20 liters of 20% sugar solution so that the resultant solution contains 8% sugar?


20 लीटर विलयन में 20% शक्कर है। इसमें कितना जल मिलाया जाये ताकि प्राप्त विलयन में 8% शक्कर हो?

A)
10 liter

B)
20 liter

C)
24 liter

D)
30 liter


Correct Answer :

30 liter


Explanation :

Initial Solution = 20 liters(water+sugar)
Initial sugar=20%
So, Initial Water=80% of 20 = 16

Let x is the water to be added to the mixture so that the new mixture must have ontains 8% sugar i.e. 92% water

Thus,new Solution = 20+x
water in new Solution = 16+x

16+x = 92% of (20+x)
16+x = (92/100)*(20+x)
16+x = (23/25)*(20+x)

400+25x=460+23x
2x = 60
x = 30 L

In 1 litre mixture of sprit and water, 20% is water. How much sprit should be added, so that the proportion of water becomes 5%?


स्प्रिट और पानी के 1 लीटर विलयन में 20% पानी है। कितनी स्प्रिट और मिलाई जाये ताकि पानी कि मात्रा 5% हो जाये?

A)
3 litres

B)
4 litres

C)
5 litres

D)
6 litres


Correct Answer :

3 litres

There are two types of mixture of milk and water. In the first mixture, out of 27 ltr, 24 ltr is milk only and in the second mixture, 40 ltr is milk and 5 ltr is water. Which one mixture is better in terms of milk’s strength?


दूध तथा पानी के दो प्रकार के मिश्रण है । पहले मिश्रण के 27 लीटर में, 24 लीटर केवल दूध है तथा दूसरे मिश्रण में 40 लीटर दूध तथा 5 लीटर पानी है । कौन­से मिश्रण में दूध की अच्छी मात्रा है ?

A)
First

B)
Second

C)
Same in both

D)
Data insufficient


Correct Answer :

Same in both

An ore contains 25% of an alloy that has 90% copper. Other than this, in the remaining 75% of the ore, there is no copper. How many kilograms of the ore are needed to obtain 60 kg of pure copper?


एक अय‫स्क‬ के 25% में एक मिश्र धातु है जिसमें 90% ताँबा है । इसके शेष 75% अय‫स्क‬ में ताँबा नहीं है । 60 किग्रा शुद्ध ताँबा प्राप्त करने के लिये कितने किलोग्राम अय‫स्क‬ की आवश्यकता होगी?

A)
250

B)
275

C)
300

D)
266.66


Correct Answer :

266.66


Explanation :

Let there is 100 kg ore.
25% of ore contains 90% copper,which means 25 kg contains; 25*90/100 = 22.5 kg of copper.

22.5 kg copper included in 100 kg of ore.
Then, 1 kg of copper = 25/100 kg ore contains
Hence, 60 kg copper = 100*60/22.5 = 266.66 kg of ore contains

The ratio of two liquids in a mixture is 3 : 5 and that in another mixture is 6:1. In what ratio these two mixtures must be mixed so as to make the ratio of the two liquids 7:3?


एक मिश्रण में दो द्रवों का अनुपात 3:5 है और दूसरे मिश्रण में 6:1 है । इन दो मिश्रणों को किस अनुपात में मिलाना चाहिए कि दो द्रवों का अनुपात 7:3 हो जाए?

A)
44 : 61

B)
44 : 71

C)
44 : 81

D)
44 : 91


Correct Answer :

44 : 91


Explanation :

By the rule of alligation: If two ingredients are mixed, then
Quantity of cheaper/Quantity of dearer =[(C.P. of dearer) - (Mean price)] / (Mean price) - [(C.P. of cheaper)]

i.e. (Cheaper Quantity):(Dearer quantity)= (d-m):(m-c).

ratio of a liquid1 in mixture1, c=3/8
ratio of a liquid1 in mixture2, d=6/7
Mean ratio of a liquid1 or ratio of a liquid1 in resultant mixture, m= 7/10

Thus ,Required ratio = (6/7 - 7/10) / (7/10 - 3/8)
= ((60-49)/70) / ((28-15)/40)
=(11/70) / (13/40)
=(11*40) / (70*13)
=44 / 91

A mixture of 40 litres of milk and water contains 10% water. How much water should be added so that the water is 20% in the new mixture?


40 लीटर दूध और पानी का मिश्रण में 10% पानी है। मिश्रण में कितना पानी जोडे ताकि नए मिश्रण में पानी 20% हो जाएं?

A)
4 L

B)
7 L

C)
5 L

D)
8 L


Correct Answer :

5 L


Explanation :

Initial Solution = 40
Initial water =10% of 40 = 4

Let x water be added then the new mixture must have 20% water

Final Solution = 40+x
Final water = 4+x

4+x = 20% of (40+x )
4+x = (20/100)*(40+x )
4+x = (1/5)*(40+x )
20+5x=40+x
4x=20
x = 5
water to be added to the mixture, x = 5

In Jar A, 180 L milk was mix with 36 L water.Some of this mixture was taken out from Jar A and put it in Jar B. If after adding 6 L of water in the mixture, the respective ratio between milk and water in Jar B was 5 : 2 respectively, what was the amount of mixture that was taken out from Jar A?


जार A में, 180 L दूध तथा 36 L पानी मिश्रण था। जार A कुछ मिश्रण निकाल कर जार B में डाल गया। यदि मिश्रण में 6 L पानी जोड़ने के बाद, तब जार B मे दूध और पानी के बीच संबंधित अनुपात क्रमशः 5: 2 हे, जार A से बाहर निकाले गए मिश्रण की मात्रा क्या थी?

A)

24


B)

54


C)

30


D)

36



Correct Answer :

36


Explanation :

Ratio of milk and water in jar A = 180 L : 36 L = 5 : 1
Let, x L of mixture taken out from jar A.

So, Quantity of milk taken out from jar A = x*5/6 = 5x/6
and Quantity of water taken out from jar A = x*1/6 = x/6

Now, according to the question,
(5x/6) / (x/6 + 6) = 5/2
(5x/6) / (x + 36)/6 = 5/2
5x / (x + 36) = 5/2
10x = 5x + 180
5x = 180
x = 36
Hence, 36 L of mixture was taken out from Jar A.

25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is the ratio 1 : 2 and the amount of lead and tin in the alloy Y is in the ratio 2 : 3, then what is the ratio of lead to tin in the mixture?


25 किलो मिश्र धातु X को 125 किलोग्राम मिश्र धातु Y के साथ मिलाया जाता है। यदि मिश्र धातु X में लेड(सीसा ) और टिन(रागाँ) की मात्रा का अनुपात 1: 2 और मिश्र धातु Y में लेड और टिन की मात्रा का अनुपात 2: 3 है। तो मिश्रण में टिन और लेड का अनुपात क्या है?

A)
1 : 2

B)
2 : 3

C)
3 : 5

D)
7 : 11


Correct Answer :

7 : 11


Explanation :

Alloy X
Total 25
Ratio 1:2
lead 25* (1/3)=25/3
tin 25* (2/3)=50/3

Alloy Y
Total 125
Ratio 2:3
lead 125* (2/5)=50
tin 125* (3/5)=75

When X and Y are mixed, then
Amount of lead = (25/3) + 50 = 175/3 kg
Amount of tin = (50/3) + 75 = 275/3 kg

Ratio of lead to tin in the mixture = (175/3) / (275/3) = 175 : 275 = 7 : 11

In what ratio must Rs 50 per kg salt be mixed with Rs 80 per kg salt to obtain a mixture worth of Rs 60 per kg?


50 रुपये प्रति किलो नमक को 80 रुपये प्रति किलो नमक मे किस अनुपात में मिलाया जाए कि प्राप्त मिश्रण की कीमत 60 रुपये प्रति किलो हो जाए?

A)

1 : 2


B)

2 : 1


C)

1 : 1


D)

3 : 2



Correct Answer :

2 : 1


Explanation :

The Required ratio = cp of biggest - mean price / mean price- cp of lowest
=(80 – 60)/(60- 50)
=20:10
=2:1

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