Question

Three persons P, Q, R can complete a work in 36 days and earn Rs.5400. The same work will be completed by P, R in 20 days and earn Rs.1880, whereas Q, R can complete the work in 40 days and charge Rs.3040. The amount R charges to work for 1 day (in rupees) is

• A. \(25\)
• B. \(24\)
• C. \(20\)
• D. \(18\)

Hint:

Convert total earnings into daily earnings first. Then form equations and solve.

Answer 1

The Correct Option is C

Concept: Charges are proportional to work done. Let the total work be: \[ 1 \]

Step 1: Find total daily charges.
P, Q, R together complete in: \[ 36 \text{ days} \] Total amount: \[ 5400 \] So daily combined charge: \[ \frac{5400}{36}=150 \] Thus: \[ P+Q+R=150 \quad ...(1) \]

Step 2: Find P and R daily charges.
P, R complete in: \[ 20 \text{ days} \] Total amount: \[ 1880 \] Daily charge: \[ \frac{1880}{20}=94 \] Thus: \[ P+R=94 \quad ...(2) \]

Step 3: Find Q and R daily charges.
Q, R complete in: \[ 40 \text{ days} \] Total amount: \[ 3040 \] Daily charge: \[ \frac{3040}{40}=76 \] Thus: \[ Q+R=76 \quad ...(3) \]

Step 4: Solve for R.
Add (2) and (3): \[ P+Q+2R=170 \] From (1): \[ P+Q+R=150 \] Subtract: \[ R=20 \] Thus, R charges per day: \[ \boxed{20} \]