Ratio, Proportion
- When the market price per kg of rice and wheat be in the ratio 3 : 2 , the monthly expenses of a family towards rice and wheat are in the ratio 5 : 6 . If the market price of rice and wheat becomes in the ratio 4 : 3 , what will be the ratio of expenses towards them ? (Assume that amount of rice and wheat consumed remains unaltered .)
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Market price per kg :
Rice = Rs . 3x
Wheat = Rs . 2x
Monthly expenses :
Rice = Rs . 5y
Wheat = Rs . 6yAmount of rice = 5y kg 3x Amount of wheat = 6y kg 2x
New price :
Rice = Rs . 4z / kg
Wheat = Rs . 3z / kg
∴ Required ratio= 5y " 4z : 6y " 3z 3x 2x = 20 : 18 3 2
= 20 : 27Correct Option: B
Market price per kg :
Rice = Rs . 3x
Wheat = Rs . 2x
Monthly expenses :
Rice = Rs . 5y
Wheat = Rs . 6yAmount of rice = 5y kg 3x Amount of wheat = 6y kg 2x
New price :
Rice = Rs . 4z / kg
Wheat = Rs . 3z / kg
∴ Required ratio= 5y " 4z : 6y " 3z 3x 2x = 20 : 18 3 2
= 20 : 27
- The ratio of the radii of two cylinders is 2 : 3, and the ratio of their heights is 5 : 3. The ratio of their volumes will be
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r1 = 2 and h1 = 5 r2 3 h2 3 ∴ Ratio of volumes of cylinders = πr12h1 πr22h2 = 
r1 
2 × h1 r2 h2 = 2 2 × 5 3 3 = 20 27 Correct Option: B
r1 = 2 and h1 = 5 r2 3 h2 3 ∴ Ratio of volumes of cylinders = πr12h1 πr22h2 = r1 2 × h1 r2 h2 = 2 2 × 5 3 3 = 20 27
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But by mistake it was divided in the ratio of 4 : 5 : 6. The amount in excess received by C was₹ 555 was to be divided among A, B and C in the ratio of 1 : 1 : 1 . 4 5 6
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Case I
A : B : C = 1 : 1 : 1 4 5 6 = 1 × 60 : 1 × 60 : 1 × 60 4 5 6
[ LCM of 4, 5 and 6 = 60]
= 15 : 12 : 10
Sum of ratios = 15 + 12 + 10 = 37∴ C’s share = 10 × 555 37
= ₹ 150
Case II
A : B : C = 4 : 5 : 6
Sum of ratios = 4 + 5 + 6 = 15∴ C’s share = 6 × 555 15
= ₹ 222
∴ Required answer
= ₹ (222 – 150) = ₹ 72Correct Option: A
Case I
A : B : C = 1 : 1 : 1 4 5 6 = 1 × 60 : 1 × 60 : 1 × 60 4 5 6
[ LCM of 4, 5 and 6 = 60]
= 15 : 12 : 10
Sum of ratios = 15 + 12 + 10 = 37∴ C’s share = 10 × 555 37
= ₹ 150
Case II
A : B : C = 4 : 5 : 6
Sum of ratios = 4 + 5 + 6 = 15∴ C’s share = 6 × 555 15
= ₹ 222
∴ Required answer
= ₹ (222 – 150) = ₹ 72
- The ratio of weekly income of A and B is 9 : 7 and the ratio of their expenditures is 4 : 3. If each saves ₹ 200 per week, then the sum of their weekly income is
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Let A’s and B’s weekly income be ₹ 9x and ₹ 7x and their expenditures be ₹ 4y and 3y respectively.
Then, 9x – 4y = 200 ...(i)
and 7x – 3y = 200 ...(ii)
⇒ 9x – 4y = 7x – 3y
⇒ 9x – 7x = 4y – 3y
⇒ 2x = y ...(iii)
From equation (i),
9x – 4y = 200
⇒ 9x – 8x = 200
⇒ x = 200
∴ Sum of their weekly income
= 16x = 16 × 200 = ₹ 3200Correct Option: B
Let A’s and B’s weekly income be ₹ 9x and ₹ 7x and their expenditures be ₹ 4y and 3y respectively.
Then, 9x – 4y = 200 ...(i)
and 7x – 3y = 200 ...(ii)
⇒ 9x – 4y = 7x – 3y
⇒ 9x – 7x = 4y – 3y
⇒ 2x = y ...(iii)
From equation (i),
9x – 4y = 200
⇒ 9x – 8x = 200
⇒ x = 200
∴ Sum of their weekly income
= 16x = 16 × 200 = ₹ 3200
- Alcohol and water in two vessels A and B are in the ratio 5 : 3 and 5 : 4 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C in the ratio 7 : 5 ?
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By Alligation Rule
∴ Ratio = 1 : 1 36 24
= 3 : 2Correct Option: B
By Alligation Rule
∴ Ratio = 1 : 1 36 24
= 3 : 2
