Ratio, Proportion
- 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
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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
- 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
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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
- 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
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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
- There are three bottles of mixture of syrup and water of ratios 2 : 3, 3 : 4 and 7 : 5. 10 litres of the first and 21 litres of the second bottles are taken. How much quantity from third bottle is to be taken so that final mixture from three bottles will be of ratios 1 : 1.
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NA
Correct Option: D
NA
- The income of A, B and C are in the ratio 7 : 9 : 12 and their spendings are in the ratio 8 : 9 : 15. If A saves (1/4)th of his income, then the savings of A, B and C are in the ratio of :
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Income of A = ₹ 7x ;
B = ₹ 9x and C = ₹ 12x
Expenses of A = ₹ 8y ;
B = ₹ 9y and C = ₹ 15y∴ 7x – 8y = 1 × 7x 4 ⇒ 7x – 7x = 8y 4 ⇒ 21x = 8y ⇒ 21x = 32y. 4 ∴ A’s saving = 1 × 7x 4 = 1 × 32 y = 8 y 4 3 3
B’s saving = 9x – 9y= 9 × 32 y − 9y 21 = 96y − 63y 7 = 33y 7
C’s saving = 12 x – 15 y= 12 × 32 y − 15y 21 = 128y − 105y 7 = 23y 7
∴ Required ratio= 8 y : 33 y : 23 y 3 7 7
= 56 : 99 : 69Correct Option: A
Income of A = ₹ 7x ;
B = ₹ 9x and C = ₹ 12x
Expenses of A = ₹ 8y ;
B = ₹ 9y and C = ₹ 15y∴ 7x – 8y = 1 × 7x 4 ⇒ 7x – 7x = 8y 4 ⇒ 21x = 8y ⇒ 21x = 32y. 4 ∴ A’s saving = 1 × 7x 4 = 1 × 32 y = 8 y 4 3 3
B’s saving = 9x – 9y= 9 × 32 y − 9y 21 = 96y − 63y 7 = 33y 7
C’s saving = 12 x – 15 y= 12 × 32 y − 15y 21 = 128y − 105y 7 = 23y 7
∴ Required ratio= 8 y : 33 y : 23 y 3 7 7
= 56 : 99 : 69
