Ratio, Proportion
- In what proportion must a grocer mix sugar at Rs.12 a kg and Rs.7 a kg so as to make a mixture worth Rs. 8 a kg.?
-
View Hint View Answer Discuss in Forum
By the rule of alligation,
∴ Required ratio = 1 : 4Correct Option: B
By the rule of alligation,
∴ Required ratio = 1 : 4
- Three containers have their volumes in the ratio 3 : 4 : 5. They are full of mixtures of milk and water. The mixtures contain milk and water in the ratio of (4 :1), (3 : 1) and (5 : 2) respectively. The contents of all these three containers are poured into a fourth container. The ratio of milk and water in the fourth container is
-
View Hint View Answer Discuss in Forum
Let the volumes of three containers be 3 litres, 4 litres and 5 litres respectively.
Container–IMilk = 4 × 3 = 12 litres, 5 5 Water = 3 litre 5
Container–IIMilk = 4 × 3 = 3 litres, 4
Water = 1 litre
Container–IIIMilk = 5 × 5 = 25 litres 7 7 Water = 10 litres 7
∴ Required ratio in container–IV= 
12 + 3 + 25 
: 3 + 1 + 10 5 7 5 7 = 84 + 105 + 125 : 21 + 35 + 50 35 35 = 314 : 106 35 35
= 157 : 53Correct Option: C
Let the volumes of three containers be 3 litres, 4 litres and 5 litres respectively.
Container–IMilk = 4 × 3 = 12 litres, 5 5 Water = 3 litre 5
Container–IIMilk = 4 × 3 = 3 litres, 4
Water = 1 litre
Container–IIIMilk = 5 × 5 = 25 litres 7 7 Water = 10 litres 7
∴ Required ratio in container–IV= 12 + 3 + 25 : 3 + 1 + 10 5 7 5 7 = 84 + 105 + 125 : 21 + 35 + 50 35 35 = 314 : 106 35 35
= 157 : 53
- 49 kg of blended tea contains Assam and Darjeeling tea in the ratio 5 : 2. Then the quantity of Darjeeling tea to be added to the mixture to make the ratio of Assam to Darjeeling tea 2 : 1 is
-
View Hint View Answer Discuss in Forum
In 49 kg. of mixture,
Tea of Assam ⇒ 5 × 49 kg. = 35 kg. 7
Tea of Darjeeling ⇒ (49 – 35) kg. = 14 kg.
Let x kg. of Darjeeling tea be added.∴ 35 = 2 14 + x 1
⇒ 28 + 2x = 35
⇒ 2x = 35 – 28 = 7⇒ x = 7 = 3.5 kg. 2 Correct Option: B
In 49 kg. of mixture,
Tea of Assam ⇒ 5 × 49 kg. = 35 kg. 7
Tea of Darjeeling ⇒ (49 – 35) kg. = 14 kg.
Let x kg. of Darjeeling tea be added.∴ 35 = 2 14 + x 1
⇒ 28 + 2x = 35
⇒ 2x = 35 – 28 = 7⇒ x = 7 = 3.5 kg. 2
- A mixture contains spirit and water in the ratio of 3 : 2. If it contains 3 litres more spirit than water, the quantity of spirit in the mixture is
-
View Hint View Answer Discuss in Forum
Let the quantity of spirit in the mixture be x litres.
∴ Quantity of water
= (x – 3) litres
According to the question,x = 3 x − 3 2
⇒ 3x – 9 = 2x
⇒ 3x – 2x = 9
⇒ x = 9 litresCorrect Option: C
Let the quantity of spirit in the mixture be x litres.
∴ Quantity of water
= (x – 3) litres
According to the question,x = 3 x − 3 2
⇒ 3x – 9 = 2x
⇒ 3x – 2x = 9
⇒ x = 9 litres
- A vessel contains 60 litres of milk. 12 litres of milk is taken out from it and replaced by water. Then again from mixture, 12 litres is again taken out and replaced by water. The ratio of milk and water in the resultant mixture is :
-
View Hint View Answer Discuss in Forum
Remaining amount of milk = Initial quantity
= 1 − quantity taken out n Initial quantity = 60 1 − 12 2 60 = 60 1 − 1 2 5 = 60 × 4 × 4 5 5
= 38.4 litres
Quantity of water = 60 – 38.4
= 21.6 litres
∴ Required ratio
= 38.4 : 21.6 = 16 : 9Correct Option: B
Remaining amount of milk = Initial quantity
= 1 − quantity taken out n Initial quantity = 60 1 − 12 2 60 = 60 1 − 1 2 5 = 60 × 4 × 4 5 5
= 38.4 litres
Quantity of water = 60 – 38.4
= 21.6 litres
∴ Required ratio
= 38.4 : 21.6 = 16 : 9
