Question 1

A person bought 60 quintals of rice of two different sorts for Rs. 4642·50. The better sort costs Rs. 80 per quintal and the worse Rs. 75·50 per quintal. How many quintals were there of each sort?

Accepted Answer

Question 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 liter mixtures, so that the percentage of unleaded petrol becomes 5 %?

Accepted Answer

Question 3

In a mixture of 60 liters, the ratio of milk and water is 2 : 1. If the ratio of the milk and water is to be 1 : 2, then the amount of water to be further added is —

Accepted Answer

Question 4

4 vessels of equal sizes contains mixture of spirit and water. The concentration of spirit in 4 vessels are 60 %, 70 %, 75 % and 80 % respectively. If all the 4 mixtures are mixed, find in the resultant mixture the ratio of spirit to water —

Accepted Answer

Question 5

How much chicory at Rs. 24 a kg should be added to 15 kg of tea at Rs. 60 a kg as to make the mixture worth Rs. 39 a kg?

Accepted Answer

Question 6

A mixture of 150 liters of Petrol and Diesel contains 20% Diesel. How much more Diesel should be added so that Diesel becomes 25% of the new mixture?

Accepted Answer

Let us assume P liters of Diesel added to the mixture so that Diesel will be 25% in the new mixture. According to Question, Quantity of Diesel in 150 liters of the mixture = 20% of 150 = 150 x 20/100 = 30 liters. After adding P liters of Diesel, The total quantity of Diesel becomes (30 + P) and total volume of mixture will be (150 + P). Again According to Question, After adding the P liters of Diesel in the mixture, the Diesel quantity becomes 25% of the new mixture. Quantity of Diesel in new mixture = 25% of Total mixture. ⇒ (30 + P) = (150 + P) x 25 % ⇒ 30 + P = (150 + P) x 25/100 ⇒ 30 + P = (150 + P) x 1/4 ⇒ 120 + 4P = 150 + P ⇒ 4P - P = 150 - 120 ⇒ 3P = 30 ⇒ P = 10 liters.

Question 7

Two vessels A and B contain milk and water in the ratio 7 : 5 and 17 : 7 respectively. In what ratio mixtures from two vessels should be mixed to get a new mixture containing milk and water in the ratio 5 : 3?

Accepted Answer

First of all we write the fraction of milk present in three mixtures. In A : 7 /12 In B : 17 /24 In combination of A and B : 5 /8 We now apply allegation rule on these fractions from figure. So, Ratio of A: B = 2 : 1 2nd Method Let us assume P mixture taken from first vessel and Q mixture taken from second vessel to form a new mixture. Part of Milk in P mixture from first vessel = 7P/12 Part of Milk in Q mixture from Second vessel = 17Q/24 Part of Water in P mixture from first vessel = 5P/12 Part of Milk in Q mixture from Second vessel = 7Q/24 According to question, After mixing the P and Q, we will get mixture. Milk in New Mixture / Water in New Mixture = 5/3 {(7P/12) + (17Q/24 ) } /{ (5P/12) + (7Q/24) } = 5/3 {(14P + 17Q)/24 } /{ (10P + (7Q)/24 } = 5/3 {(14P + 17Q) } /{ (10P + (7Q)} = 5/3 (14P + 17Q) x 3 = 5 x (10P + (7Q) 42P + 51Q = 50P + 35Q 51Q - 35Q = 50P - 42P 8P = 16Q P = 2Q P/Q = 2 P : Q = 2 : 1

Question 8

A person covers a distance of 100 kms in 10 hours, partly by walking at 7 km/hr and rest by running at 12 km/hr. Find the distance covered in each part.

Accepted Answer

Average speed = (100 / 10) = 10 km/hr. Ratio of time taken at 7 km/hr to 12 km/hr = 2 : 3 Time taken at 7 km/hr = 2 (2 + 3) × 10 = 4 hrs. Distance covered at 7 km/hr = 7 × 4 = 28 km. Distance covered at 12 km/hr = 100 – 28 = 72 km.

Question 9

From a cask of wine containing 25 litres, 5 litres are withdrawn and the cask is refilled with water. The process is repeated a second and then a third time. Find the quantity of wine left in the cask and also the ratio of wine to water in the resul…

Accepted Answer

Here, quantity of wine left after third operation = [1 - (5 / 25)]3 x 25 = (4 / 5)3 x 25 = (64 / 125) x 25 = (64 / 5) = 12 4/5 liters. Final ratio of wine to water = (64 / 125) / (1- 64 /125) = (64 / 125) /(61 / 125) Wine : Water = (64 / 61)

Question 10

A vessel contains mixture of liquids A and B in the ratio 3: 2. When 20 litres of the mixture is taken out and replaced by 20 litres of liquid B, the ratio changes to 1: 4. How many litres of liquid A was there initially present in the vessel?

Accepted Answer

21.% of liquid B initially present in the vessel = 2 / (3 + 2) × 100 = 40% % of liquid B finally present in the vessel = 4 / (1 + 4) × 100 = 80% The second solution is liquid B which is being mixed and it has 100% liquid B. 80% of liquid B present in the resultant mixture may be taken as average percentage. So, using rule of alligation on liquid B per cent, we can write, or 1 : 2 The ratio of liquid left in the vessel to liquid B being mixed = 1: 2 Since the quantity of liquid B being mixed is 20 liters, the quantity of liquid left in the vessel is 10 liters. Therefore, the total quantity of liquid initially present in the vessel = 10 + 20 = 30 liters Quantity of liquid A = 3 / (2 + 3) × 30 = 18 liters.

Question 11

A piece of an alloy of two metals (A and B) weighs 15 gms and costs Rs. 150. If the weights of the two metals be interchanged, the new alloy would be worth Rs. 120. If the price of metal A is Rs. 6 per gm, find the weight of the other metal in the o…

Accepted Answer

If the two alloys are mixed, the mixture would contain 15 gms of each metal and it would cost Rs. (150 + 120) = Rs. 270. Cost of (15 gms of metal A + 15 gms of metal B) = Rs. 270 Cost of (1 gm of metal A + 1 gm of metal B) = Rs. (270 / 15) = Rs. 18 Cost of 1 gm of metal B = Rs. (18 – 6) = Rs. 12 Average cost of original piece of alloy = (150 / 15) = Rs. 10 per gm. Quantity of metal / A Quantity of metal B = (2 / 4) = (1 / 2) Quantity of metal B = 2 (1 + 2) × 15 = 10 gms.

Question 12

A container of 90 liters with two liquids A and B, 60% of liquid A and 30% of liquid B are taken out of the vessel. This leaves the container 40% empty. Find the initial quantity of both liquids.

Accepted Answer

Here withdrawal of liquid A and B result into making the container empty. Hence percentage of two liquids withdrawn are two components of the percentage by which the container becomes empty. Applying the rule of alligation, we get A : B = 10 : 20 or 1 : 2 Quantity of liquid = 1 (1 + 2) × 90 = 30 liters Quantity of liquid B = 90 – 30 = 60 liters.

Question 13

Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:

Accepted Answer

Here first two varieties of tea are mixed in equal ratio. So their average price = (126 + 135) /2 = Rs. 130.50 Let price of the third variety per kg be Rs. A; then now mixture is formed by two varieties one at Rs. 130.50 per kg and other at Rs. A per kg in the same ratio 2 : 2 i.e, 1 : 1 By the rule of alligation, (A - 153) / (22.50) = 1 ⇒ A – 153 = 22.50 ∴ A = Rs. 175.50

Question 14

A mixture of 20 kg of spirit and water contains 10 % water. How much water must be added to this mixture to raise the percentage of water to 25 %?

Accepted Answer

Question 15

A jar full of whisky contains 40 % of alcohol. A part of this whisky is replaced by another containing 19 % alcohol and now the percentage of alcohol was found to be 26. The quantity of whisky replaced is —

Accepted Answer

Question 16

Rs. 1000 is lent out in two parts, one at 6 % simple interest and the other at 8 % simple interest. The yearly income is Rs. 75. The sum lent at 8 % is —

Accepted Answer

Question 17

A man has whisky worth Rs. 22 a liter and another lot worth Rs. 18 a liter. Equal quantities of these are mixed with water to obtain a mixture of 50 liters worth Rs. 16 a liter. Find how much water the mixture contains?

Accepted Answer

Question 18

A man buys milk at Rs. 5 a litre and mixes it with water. By selling the mixture at Rs. 4 a litre he gains 121/2 % on his outlay. How much water did each litre of the mixture contain?

Accepted Answer

Question 19

3 glasses of capacity 2 liters, 5 liters and 9 liters contain mixture of milk and water with milk concentrations 90 %, 80 % and 70 % respectively. The contents of 3 glasses are emptied into a large vessel. Find the milk concentration and ratio of mi…

Accepted Answer

Question 20

From a cask of wine, containing 64 liters, 8 liters are drawn out and the cask is filled up with water. If the same process is repeated a second, then a third time, what will be the number of liters of wine left in the cask?

Accepted Answer

Alligation or Mixture Questions