**(01) Two vessels contain spirit and water mixed respectively in the ratio of 1: 4 and 4: 1 Find the ratio in which these are to be mixed to get a new mixture in which the ratio of spirit to water is 1: 3.**

Spirit in Solution 1= 1/ 5

Spirit in Solution 2 = 4/ 5

Spirit in mixture = 1/ 4

By rules of alligations:

so, required ratio = (11/ 20)/ (1/ 20) = 11:1

**Ans. The required ratio is 11:1**

**Qu.2 The price of a table and a chair is Rs. 3000. The table was sold at a 20% profit and the chair at a 10% loss. If in the transaction a man gains Rs. 300, how much is cost price (in Rs.) of the table?**

Overall profit = (gain/ CP) x 100

= (300/ 3000) x 100

= 10 %

n_{1 } : n_{2 } =20 : 10 = 2: 1

**CP of table** = (2/2+1) x 3000

= Rs, 2000

**Ans. CP of table is Rs. 2000**

**Qu.3 Two solutions of 80% and 87% purity are mixed resulting in 35 liters of mixture of 84% purity. How much is the quantity of the first solution in the resulting mixture?**

**(04) In the Delhi zoo, there are lions and there are hens. If the heads are counted, there are 180, while the legs are 448. What will be the number of lions in the zoo?**

Given**: **

heads = 180 legs = 448

Average legs per head = 448/ 180

Lions: hens = (88/ 120)/ (272/ 120)

= 88/ 272

Hence, the number of Lions = (88 x 180)/ (88 + 272)

= (88 x 180) / 360

= 44

**Ans. The number of lions is 44.**

**Qu.5 A bonus of Rs. 1,00,000 was divided among 500 workers of a factory. Each male worker gets 500 rupees and each female worker gets 100 rupees. Find the number of male workers in the factory.**

Given:

Total bonus = Rs. 1,00,000

Workers = 500

Average bonus per worker = Total bonus/ no. Of worker

= 1,00,000/ 500 = Rs. 200

n_{1} : n_{2 } = 100: 300 = 1: 3

Therefore, no. Of male workers in the factory = (1/ 3+1) x 500

= 125

**Ans. There are 125 male workers in the factory.**