**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.

**Alternate :**

**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 3_{x5}: 4_{x5}-> 7 LCM(7, 5, 7)=35 Mixture B 4_{x7}: 1_{x7}-> 5 Final mixture 5_{x5}: 2_{x5}-> 7

To make quantity equal of both mulitply with 7 and 5 respectively.

Milk Water 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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