Two friends A and B started a business with initial investment in the

1.	Two friends A and B started a business with initial investment in the ratio 9 : 10. After 3 months one other friend C joined the business with a capital of Rs.95000. As a result A and B withdrew same amount from their capital in the ratio of their investment. If at the end of the year total profit is Rs.21700 and A got Rs.5625, then find out A’s initial capital.1. 810002. 950003. 920004. 900005. 100000
Answer» Correct Answer - Option 4 : 90000 Given: Initial capital ratio of A and B is 9 : 10 3 months after the start C joined with Rs.95000 Year-end profit = Rs.21700 and A got = Rs.5625 Formula used: Profit = total profit × (part share / total share) Calculations: Let us assume initial capital of A and B be 9000x and 10000x respectively. After C joined, A will withdraw = 95000 × 9/19 = 45000 B will withdraw = 95000 × 10/19 = 50000 Ratio of their capital = {(9000x × 3) + (9000x – 45000) × 9} : {(10000x × 3) + (10000x – 50000) × 9} : 81000 × 9 = (36x - 135) : (40x - 150) : 243 Now, A’s profit = [(36x - 135)/(36x - 135 + 40x – 150 + 243)] × 21700 ATQ, [(36x - 135) / (36x - 135 + 40x – 150 + 243)] × 21700 = 5625 ⇒ (36x – 135) / (76x - 42) = 5625/21700 = 225/868 ⇒ x = 10 ∴ A’s initial capital = 9000 × 10 = Rs.90000

Two friends A and B started a business with initial investment in the ratio 9 : 10. After 3 months one other friend C joined the business with a capital of Rs.95000. As a result A and B withdrew same amount from their capital in the ratio of their investment. If at the end of the year total profit is Rs.21700 and A got Rs.5625, then find out A’s initial capital.1. 810002. 950003. 920004. 900005. 100000

Answer» Correct Answer - Option 4 : 90000

Given:

Initial capital ratio of A and B is 9 : 10

3 months after the start C joined with Rs.95000

Year-end profit = Rs.21700 and A got = Rs.5625

Formula used:

Profit = total profit × (part share / total share)

Calculations:

Let us assume initial capital of A and B be 9000x and 10000x respectively.

After C joined,

A will withdraw = 95000 × 9/19 = 45000

B will withdraw = 95000 × 10/19 = 50000

Ratio of their capital =

{(9000x × 3) + (9000x – 45000) × 9} : {(10000x × 3) + (10000x – 50000) × 9} : 81000 × 9

= (36x - 135) : (40x - 150) : 243

Now, A’s profit = [(36x - 135)/(36x - 135 + 40x – 150 + 243)] × 21700

ATQ,

[(36x - 135) / (36x - 135 + 40x – 150 + 243)] × 21700 = 5625

⇒ (36x – 135) / (76x - 42) = 5625/21700 = 225/868

⇒ x = 10

∴ A’s initial capital = 9000 × 10 = Rs.90000