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61. The ratio of the quantities of sugar, in which sugar costing Rs. 20 per kg and Rs. 15 per kg, should be mixed so that here will be neither loss nor gain on selling the mixed sugar at the rate of Rs. 16 per kg, is -
When there is no profit no loss,
Here, Cost price = Selling price
∴ Cost price of mixed sugar = Rs. 16/kg
Apply alligation

Solution:
According to the question,When there is no profit no loss,
Here, Cost price = Selling price
∴ Cost price of mixed sugar = Rs. 16/kg
Apply alligation

62. The proportion of acid and water in three samples is 2 : 1, 3 : 2 and 5 : 3. A mixture containing equal quantities of all three samples is made. The ratio of water and acid in the mixture is -
Solution:
According to the question,
63. A shopkeeper bought 15 kg of rice at the rate of Rs. 29 per kg and 25 kg of rice at the rate of Rs. 20 per kg. He sold the mixture of both types of rice at the rate of Rs. 27 per kg. His profit in this transaction is -
Cost price of the mixture
= 15 × 29 + 25 × 20
= Rs. 935
Selling price of the mixture
= 27 × 40
= Rs. 1080
Profit = Selling price - Cost price
Profit = 1080 - 935 = Rs. 145
Solution:
According to the question,Cost price of the mixture
= 15 × 29 + 25 × 20
= Rs. 935
Selling price of the mixture
= 27 × 40
= Rs. 1080
Profit = Selling price - Cost price
Profit = 1080 - 935 = Rs. 145
64. Lala has lent some money to Arun at 5% p.a. and Bhatia at 8% p.a. At the end of the year, he has gained an overall interest at the rate 6%. In what ratio has he lent the money to Arun and Bhatia ?

Then, Lala give loan in ratio 2 : 1, to Arun and Bhatia
Solution:
By alligation method - 
Then, Lala give loan in ratio 2 : 1, to Arun and Bhatia
65. The ratio of milk and water in mixture of four containers are 5 : 3, 2 : 1, 3 : 2 and 7 : 4 respectively. In which container is the quantity of milk, relative to water, minimum ?
Container :
∴ The quantity of milk relative to water minimum in container third
Solution:
∴According to the question,Container :
∴ The quantity of milk relative to water minimum in container third
66. In two types of stainless steel, the ratio of chromium and steel are 2 : 11 and 5 : 21 respectively. In what proportion should the two types be mixed so that the ratio of chromium to steel in the mixed type becomes 7 : 32 ?
Now using alligation,

Solution:
According to the question,Now using alligation,

67. Three containers whose volumes are in the ratio of 2 : 3 : 4 are full of mixture of spirit and water. In the 1st container the ratio of spirits and water is 4 : 1, in 2nd container the ratio is 11 : 4 and on the 3rd container ratio is 7 : 3. All the three mixtures are mixed in a big container. The ratio of spirit and water in the resultant mixture is ?
Spirit =
water =
In 3 litres of first container,
Spirit =
water =
In 4 litres of first container,
Spirit =
water =
∴ Required ratio
= 33 : 12
= 11 : 4
Solution:
In 2 litres of first container,Spirit =
water =
In 3 litres of first container,
Spirit =
water =
In 4 litres of first container,
Spirit =
water =
∴ Required ratio
= 33 : 12
= 11 : 4
68. Alcohol and water in two vessels A and B are in the ratio 5 : 3 and 5 : 4 respectively. In what ratio, the liquid of both the vessels be mixed to obtain a new mixture in vessel C in the ratio 7 : 5 ?
Now using alligation,
Solution:
According to the question,Now using alligation,

69. Two vessels A and B contains acid and water in the ratio 4 : 3 and 5 : 3 respectively. Then the ratio in which these mixtures to be mixed to obtain a new mixture in vessel C containing acid and water in the ratio 3 : 2 is -
Now using alligation,
Solution:
According to the question,Now using alligation,

70. The ratio of spirit and water in two mixtures of 20 litres and 36 litres is 3 : 7 and 7 : 5 respectively. Both the mixtures are mixed together. Now the ratio of the spirit and water in the new mixture is ?
Solution: