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Directions: Read the given information carefully and answer the following questions.
A and B invested in a business in the ratio 4 : 5. A invested for 4 months more than B. At the end of year, the total profit earned is Rs. 35000 out of which B earned Rs. 15000. 
  • a)
    3 : 2
  • b)
    5 : 3
  • c)
    2 : 1
  • d)
    4 : 1
  • e)
    5 : 2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Directions: Read the given information carefully and answer the follow...
Given information:
- A and B invested in a business in the ratio 4:5.
- A invested for 4 months more than B.
- At the end of the year, the total profit earned is Rs. 35000, out of which B earned Rs. 15000.

To find:
The ratio of the profits earned by A and B.

Solution:
Let's assume that A invested for x months and B invested for (x - 4) months.
According to the given ratio, the investment of A and B can be represented as:
A's investment = (4/9) * Total investment
B's investment = (5/9) * Total investment

Total profit earned by A:
= (A's investment) * (A's time period) * (B's share of profit)
= ((4/9) * Total investment) * x * (15/35) [As B earned Rs. 15000 out of the total profit of Rs. 35000]
= (4x/9) * (15/35) * Total investment

Total profit earned by B:
= (B's investment) * (B's time period) * (B's share of profit)
= ((5/9) * Total investment) * (x - 4) * (15/35)
= (5(x - 4)/9) * (15/35) * Total investment

Given that the total profit earned is Rs. 35000, we can write the equation as:
(4x/9) * (15/35) * Total investment + (5(x - 4)/9) * (15/35) * Total investment = 35000

Simplifying the equation:
60x/315 + 75(x - 4)/315 = 35000
(60x + 75x - 300)/315 = 35000
(135x - 300)/315 = 35000
135x - 300 = 35000 * 315
135x - 300 = 11025000
135x = 11025300
x = 81780/135
x ≈ 606.22

Since x represents the number of months, it cannot be in decimal form. Therefore, we round it off to the nearest whole number.
x ≈ 606

Therefore, A invested for approximately 606 months and B invested for (606 - 4) = 602 months.

The ratio of their investments is 4:5, so the ratio of their profits will be the same.

Therefore, the ratio of the profits earned by A and B is 4:5, which can be simplified to 5:3.
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Directions: Read the given information carefully and answer the following questions.A and B invested in a business in the ratio 4 : 5. A invested for 4 months more than B. At the end of year, the total profit earned is Rs. 35000 out of which B earned Rs. 15000.a)3 : 2b)5 : 3c)2 : 1d)4 : 1e)5 : 2Correct answer is option 'B'. Can you explain this answer?
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