Question

₹4200 are divided among ‘P’, ‘Q’, ‘R’ and ‘S’ in such a way that the shares of ‘P’ and ‘Q’. ‘Q’ and ‘R’ as well ‘R’ and ‘S’ are in the ratios of 2:3, 4:5 and 6:7 respectively, the share of ‘P’ is :

• A. ₹ 600
• B. ₹ 640
• C. ₹ 1280
• D. ₹ 1480

Answer 1

The Correct Option is B

To solve this problem, we need to distribute ₹4200 among ‘P’, ‘Q’, ‘R’, and ‘S’ based on the given ratios:

1. The ratio of P and Q is 2:3. Assume P's share is 2x and Q's share is 3x.
2. The ratio of Q and R is 4:5. Assume Q's share is 4y and R's share is 5y. But since Q's share is common in both ratios, 3x=4y. Thus, x = (4/3)y.
3. The ratio of R and S is 6:7. Assume R's share is 6z and S's share is 7z. But R's share is common, hence 5y=6z. Thus, y = (6/5)z.

Now substituting y = (6/5)z into x = (4/3)y, we get:

• x = (4/3) * (6/5)z = (24/15)z = (8/5)z

The total amount to be distributed is:

• P + Q + R + S = 2x + 3x + 5y + 7z = 5x + 5y + 7z

Now using the relationships found:

• 5x = 5((8/5)z) = 8z
• 5y = 6z

Substituting:

• P + Q + R + S = 8z + 6z + 6z + 7z = 27z

We have:

• 27z = 4200

Solving for z, we get:

• z = 4200/27 = 155.56

Now find P's share:

• P = 2x = 2((8/5)z) = (16/5)z
• P = (16/5)*155.56 ≈ 640

Thus, the share of ‘P’ is ₹640.