Rs.9400 is distributed among P, Q, R in such a way that if Rs.93, Rs.24, Rs.55 are deducted from their respective shares, then they have money in the ratio 3:4:5. What is the share of P?

Correct option is A

Given:

Total amount = ₹ 9400

After deductions, the ratio of shares is 3 ∶ 4 ∶ 5

Deductions: ₹ 93 from P's share, ₹ 24 from Q's share, ₹ 55 from R's share

Concept Used:

Use the concept of ratios and linear equations to solve for individual shares.

Solution:

Let the shares of P, Q, and R be p, q, and r respectively.

Given, (p - 93) ∶ (q - 24) ∶ (r - 55) = 3 ∶ 4 ∶ 5

Assume k is the constant of proportionality.

=> p - 93 = 3k

=> q - 24 = 4k

=> r - 55 = 5k

Total amount: p + q + r = 9400

Substitute the values of p, q, and r:

=> (3k + 93) + (4k + 24) + (5k + 55) = 9400

=> 3k + 4k + 5k + 93 + 24 + 55 = 9400

=> 12k + 172 = 9400

=> 12k = 9400 - 172

=> 12k = 9228

=> k = 9228 / 12

=> k = 769

Find the share of P:

=> p = 3k + 93

=> p = 3 × 769 + 93

=> p = 2307 + 93

=> p = 2400

∴ The share of P is ₹ 2307.