Question 1: 30 litres of a mixture of milk and water contains 10% of water, the water to be added, to make the water content 25% in the new mixture. Find how many litres water will be added?
Solution : Water in the 30 litre of mixture = 30 x 10/100 = 3 litres
Milk in the mixture = 30 – 3 = 27 litres
Let x litres of water is mixed.
Acc. to question
(3 + x)/(30 + x) = 25/100
4(3 + x) = 30 + x
12 + 4x = 30 + x
3x = 18
x = 6
Hence, 6 litres of water to be added in the mixture.
Question 2: 25000 students appeared in an exam. 60% of the boys and 40% of the girls cleared the examination. If the total percent of students qualifying is 55%, how many girls appeared in the exam?
Solution : By alligation method
4 -> 25000
1 -> 6250
Hence, number of girls passed in the exam is 6250.
Question 3: In what ratio must a shopkeeper mix sugar at Rs 30/kg and Rs 32.5/kg, so that by selling the mixture at Rs 34.1/kg he may gain 10%.
Solution : Acc. to question
SP of 1 kg of mixture = Rs 34.1
Profit = 10% = 10/100 = 1/10
SP = 1 + 10 = 11 unit
11 units ->34.1
1 unit -> 3.1
10 unit -> 31
We obtain the CP of the mixture Rs 31.
To obtain the ratio use alligation method
Hence, the ratio in which he mixed is 3:2
Question 4: Two vessels A and B contain mixture of milk and water in ratios 3:4 and 4:1 respectively. In what ratio should quantities of mixture be taken from A and B to form a mixture in which milk to water is in the ratio 5:2?
Solution :Acc. to question
Milk Water total
Mixture A 3x5 : 4x5 -> 7 LCM(7, 5, 7)=35
Mixture B 4x7 : 1x7 -> 5
Final mixture 5x5 : 2x5 -> 7
To make quantity equal of both multiply with 7 and 5 respectively.
Mixture A 15 : 20
Mixture B 28 : 7
Final mixture 25 : 10
To obtain the ratio in which A and B mixed we apply alligation rule
Hence, the required ratio is 3:10.
Question 5: 40 kg of an alloy mixed with 100 kg of alloy B. If alloy A has lead and copper in the ratio 3:2 and alloy B has copper and tin in the ratio 1:3., then the amount of copper in the new alloy is
Solution :Alloy A 40 kg contains lead and copper in ratio 3:2
So, 3+2 = 5
5 unit -> 40
1 unit -> 8
2 unit -> 16
Amount of copper in alloy A is 16 kg.
Alloy B contains copper and tin in ratio 1:3
So, 1+3 = 4
4 unit -> 100
1 -> 25
Amount of copper in alloy B is 25 kg
Hence, amount of copper in the new alloy is 16 + 25 = 41 kg.
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