Ratio, Proportion
- A and B start an enterprise together, with A as active partner. A invests Rs. 4000 and Rs. 2000 more after 8 months. B invests Rs. 5000 and withdraws Rs. 2000 after 9 months. Being the active partner, A takes Rs. 100 per month as allowance, from the profit. What is the share of B if the profit for the year is Rs. 6700?
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Ratio of the equivalent capitals of A and B for 1 month
= (4000 × 8 + 6000 × 4) : (5000 × 9 + 3000 × 3)
= (32000 + 24000) : (45000 + 9000)
= 56000 : 54000 = 28 : 27
Sum of the terms of ratio
= 28 + 27 = 55
A is an active partner.
Allowance got by A in 1 year = Rs. 1200
Remaining profit = Rs. (6700 – 1200) = Rs. 5500∴ B’s share = Rs. 
27 × 5500 
= Rs. 2700 55 Correct Option: C
Ratio of the equivalent capitals of A and B for 1 month
= (4000 × 8 + 6000 × 4) : (5000 × 9 + 3000 × 3)
= (32000 + 24000) : (45000 + 9000)
= 56000 : 54000 = 28 : 27
Sum of the terms of ratio
= 28 + 27 = 55
A is an active partner.
Allowance got by A in 1 year = Rs. 1200
Remaining profit = Rs. (6700 – 1200) = Rs. 5500∴ B’s share = Rs. 27 × 5500 = Rs. 2700 55
- A sum of Rs. 730 was divided among A, B and C in such a way that if A gets Rs. 3 then B gets Rs. 4 and if B gets Rs. 3.50 then C gets Rs. 3. The share of B exceeds that of C by
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According to the question,
A : B = 3 : 4
B : C = 3.5 : 3
= 7 : 6
∴ A : B : C
= 3 × 7 : 4 × 7 : 4 × 6 = 21 : 28 : 24
Sum of the terms of ratio = 21 + 28 + 24 = 73
∴ Difference between the shares of B and C= Rs. 28 − 24 × 730 73
= Rs. 40Correct Option: B
According to the question,
A : B = 3 : 4
B : C = 3.5 : 3
= 7 : 6
∴ A : B : C
= 3 × 7 : 4 × 7 : 4 × 6 = 21 : 28 : 24
Sum of the terms of ratio = 21 + 28 + 24 = 73
∴ Difference between the shares of B and C= Rs. 28 − 24 × 730 73
= Rs. 40
- A sum of Rs. 770 has been divided among A, B and C in such a way that A receives (2/9)th of what B and C together receive. Then A’s share is
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A’s share = 2 of (B + C)’s share 9 ∴ (B + C)’s share = 9 A’s share 2
According to the question,A + 9A = 770 2 ⇒ 2A + 9A = 770 2 ⇒ 11A = 770 2 ⇒ A = 770 × 2 = Rs. 140 11 Correct Option: A
A’s share = 2 of (B + C)’s share 9 ∴ (B + C)’s share = 9 A’s share 2
According to the question,A + 9A = 770 2 ⇒ 2A + 9A = 770 2 ⇒ 11A = 770 2 ⇒ A = 770 × 2 = Rs. 140 11
- A, B and C together start a business. Three times the investment of A equals four times the investment of B and the capital of B is twice that of C. The ratio of share of each in the profit is
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According to the question,
3A = 4B⇒ A = B ⇒ A : B = 4 : 3 4 3
B’s capital is twice C’s capital.∴ B = 2 C 1
B : C = 2 : 1
∴ A : B : C = 4 × 2 : 3 × 2 : 3 × 1
= 8 : 6 : 3Correct Option: D
According to the question,
3A = 4B⇒ A = B ⇒ A : B = 4 : 3 4 3
B’s capital is twice C’s capital.∴ B = 2 C 1
B : C = 2 : 1
∴ A : B : C = 4 × 2 : 3 × 2 : 3 × 1
= 8 : 6 : 3
- If a certain amount is fully distributed among A, B and C in such a way that A receives 1/2 of the amount, B receives 1/3 of the amount and C receives Rs. 1200, then how much money would A receive ?
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Let total amount be Rs. x.
According to the question,x + x + 1200 = x 2 3 ⇒ x – x – x = 1200 2 3 ⇒ 6x – 3x – 2x = 1200 6 ⇒ x = 1200 ⇒ x = 1200 × 6 6
= Rs. 7200∴ A’s share = Rs. 7200 = Rs. 3600 2 Correct Option: C
Let total amount be Rs. x.
According to the question,x + x + 1200 = x 2 3 ⇒ x – x – x = 1200 2 3 ⇒ 6x – 3x – 2x = 1200 6 ⇒ x = 1200 ⇒ x = 1200 × 6 6
= Rs. 7200∴ A’s share = Rs. 7200 = Rs. 3600 2
