Three friends A, B, C invested in a business in the ratio of 3 ∶ 2 ∶ 6. After 6 months C withdraw half his capital. If the total profit earned for the year is Rs.53010 (in Rs.).Then Profit made by A is

Given :

The ratio of investments of A  B and C = 3 : 2 : 6

After 6 months C withdraws half of his capital

Total profit earned in the year = Rs. 53010

Concept:

Investment = Capital x Duration of investment (in months)

Ratio of profits = Ratio of investments around 1 year

Calculation :

Let, the initial capital of A, B and C be 3a, 2a, and 6a

Now, Investment of A for 1 year = 12 x 3a = 36a

Investment of B for 1 year = 12 x 2a = 24a

According to the given data, C invested 6a for the first 6 months and 3a for the next 6 months.

Investment of C for 1 year = 6 x 6a + 6 x 3a = 54a 

Now, Ratio of their profits = 36a : 24a : 54a = 6 : 4 : 9

∴ Profit made by A = \(\dfrac{6}{6+4+9}× 53010 \)

⇒ \(\dfrac{6}{19}\) × 53010 = Rs. 16740

∴ The profit made by A is Rs. 16740.

Shortcut TrickRatio of their profits = \(12× 3:12×2:6(6+3) = 6:4:9\)

Profit of A = \(\dfrac{6}{19}× 53010 = 16740\)

Mistake Points According to the given data, C invested his initial amount for 6 months and after that, he withdrew half of his initial amount.