Ratio, Proportion
- 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 ?
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By Alligation Rule
= 15 − 14 = 1 = 7 − 6 = 1 78 78 39 39
∴ Required ratio = 1 : 2Correct Option: C
By Alligation Rule
= 15 − 14 = 1 = 7 − 6 = 1 78 78 39 39
∴ Required ratio = 1 : 2
- A and B are two alloys of gold and copper in the ratio 7 : 2 and 7:11 respectively. If equal quantities of these two alloys are melted to form a new alloy C, then the ratio of gold and copper in C is
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1 kg of each mixture is taken.
A ⇒ 7 : 2 = 14 : 4Gold = 14 ; Copper = 4 18 18
B ⇒ 7 : 11Gold = 7 ; Copper = 11 18 18
∴ Required ratio= 
14 + 7 
: 4 + 11 18 18 18 18
= 21 : 15 = 7 : 5Correct Option: D
1 kg of each mixture is taken.
A ⇒ 7 : 2 = 14 : 4Gold = 14 ; Copper = 4 18 18
B ⇒ 7 : 11Gold = 7 ; Copper = 11 18 18
∴ Required ratio= 14 + 7 : 4 + 11 18 18 18 18
= 21 : 15 = 7 : 5
- A Can contains a mixture of two liquids A and B in the ratio 7:5. When 9 litres of mixture are drained off and the Can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the Can initially ?
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Let the original quantity be 12x litres.
In 9 litres of the mixture,Liquid A = 7 × 9 = 21 litres 12 4 Liquid B = 5 × 9 = 15 litres 12 4
According to question,= 7x − 21 = 7/9 4 5x − 15 + 9 4 ⇒ 28x − 21 = 7 20x − 15 + 36 9 ⇒ 28x − 21 = 7 20x + 21 9 ⇒ 4x − 3 = 1 20x + 21 9
⇒ 36x – 27 = 20x + 21
⇒ 36x – 20x = 21 + 27
⇒ 16x = 48
⇒ x = 3
Original quantity of liquid A
= 7x = 7 × 3 = 21 litresCorrect Option: C
Let the original quantity be 12x litres.
In 9 litres of the mixture,Liquid A = 7 × 9 = 21 litres 12 4 Liquid B = 5 × 9 = 15 litres 12 4
According to question,= 7x − 21 = 7/9 4 5x − 15 + 9 4 ⇒ 28x − 21 = 7 20x − 15 + 36 9 ⇒ 28x − 21 = 7 20x + 21 9 ⇒ 4x − 3 = 1 20x + 21 9
⇒ 36x – 27 = 20x + 21
⇒ 36x – 20x = 21 + 27
⇒ 16x = 48
⇒ x = 3
Original quantity of liquid A
= 7x = 7 × 3 = 21 litres
- The ratio of milk and water in mixtures 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 ?
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Milk in first vessel = 5 = 0.625 8 Milk in second vessel = 2 = 0.66 3 Milk in third vessel = 3 = 0.6 5 Milk in fourth vessel = 7 = 0.636 11 Correct Option: C
Milk in first vessel = 5 = 0.625 8 Milk in second vessel = 2 = 0.66 3 Milk in third vessel = 3 = 0.6 5 Milk in fourth vessel = 7 = 0.636 11
- An alloy contains copper, zinc and nickel in the ratio of 5 : 3 : 2. The quantity of nickel (in kg) that must be added to 100 kg of this alloy to have the new ratio 5 : 3 : 3 is
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Let x kg of nickel be mixed.
∴ 20 + x = 3 100 + x 11
⇒ 220 + 11x = 300 + 3x
⇒ 11x – 3x = 300 – 220
⇒ 8x = 80
⇒ x = 10 kg.Correct Option: B
Let x kg of nickel be mixed.
∴ 20 + x = 3 100 + x 11
⇒ 220 + 11x = 300 + 3x
⇒ 11x – 3x = 300 – 220
⇒ 8x = 80
⇒ x = 10 kg.
