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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 -

Discuss
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
Alligation mcq solution image
Ratio 1:4
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 -

Discuss
Solution:
According to the question,

AcidWaterTotalSample I2×40=80:1×40=403×40Sample II3×24=72:2×24=485×24Sample III5×15=75_:3×15=45_8×15]120

Ratio of quantity 227:133
Required ratio = 133:227
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 -

Discuss
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 ?

Discuss
Solution:
By alligation method -
Alligation mcq solution image
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 ?

Discuss
Solution:
∴According to the question,
Container :
IIIIIIIVM:WM:WM:WM:W5:32:13:27:4

Container(I):MilkWater=53=1.67Container(II):MilkWater=21=2Container(III):MilkWater=32=1.5Container(IV):MilkWater=74=1.75

∴ 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 ?

Discuss
Solution:
According to the question,
ChromiumSteelType 12:11Type 25:21
Now using alligation,
Alligation mcq solution image
Ratio of quantity 1:2
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 ?

Discuss
Solution:
In 2 litres of first container,
Spirit = 2×45=85
water = 2×15=25

In 3 litres of first container,
Spirit =3×1115=115
water = 3×415=45

In 4 litres of first container,
Spirit =4×710=145
water = 4×310=65

∴ Required ratio
=(85+115+145):(25+45+65)
=335:125
= 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 ?

Discuss
Solution:
According to the question,
AlcoholWaterVessel A5:3Vessel B5:4
Now using alligation,
Alligation mcq solution image
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 -

Discuss
Solution:
According to the question,
AcidWaterVessel A4:3Vessel B5:3
Now using alligation,
Alligation mcq solution image
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 ?

Discuss
Solution:
According to the question,Mixture 1 = 20 litresMixture 2 = 36 litresIn Mixture 1 ratio of  SpiritWater=3710 unitsIn Mixture 2 ratio of SpiritWater=7512 units10 units 20 litres1 unit 2 litres12 units 36 litres1 unit 3 litresIn Mixture 1 ratio of SpiritWater=3×27×2=614In Mixture 2 ratio of SpiritWater=7×35×3=2115Ratio of spirits and water = 6+2114+15 = 2729 = 27:29