Question

3 women and 4 boys can earn Rs 7560 in 7 days. 11 women and 13 boys can earn Rs 30080 in 8 days. In what time (in days) will 7 women and 9 boys earn Rs 24800 ?

• A. 20
• B. 5
• C. 10
• D. 12

Hint:

Double check the arithmetic coefficients:
Notice that the target amount Rs 24800 is exactly 10 times the daily group rate Rs 2480.
In competitive exams, numbers are often chosen to divide cleanly, which can help confirm that your intermediate steps are correct.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This problem is based on the work, wages, and efficiency of different groups of workers (women and boys).
We are given the total earnings of two different combinations of women and boys over different numbers of days.
From this, we must determine the individual daily earnings of one woman and one boy, and then use those values to calculate how long it takes a third combination to earn a specific amount.

Step 2: Key Formula or Approach:
Let the daily earning of a woman be $W$ and that of a boy be $B$.
The total earnings are given by:
\[ \text{Earnings} = (\text{Number of workers} \times \text{Daily earning of each}) \times \text{Number of days} \] We can set up linear simultaneous equations to solve for $W$ and $B$.

Step 3: Detailed Explanation:

• Formulate the Equations:
- Case 1: 3 women and 4 boys earn Rs 7560 in 7 days.
Daily earning of the group:
\[ 3W + 4B = \frac{7560}{7} = 1080 \quad \text{---(Eq 1)} \]
- Case 2: 11 women and 13 boys earn Rs 30080 in 8 days.
Daily earning of the group:
\[ 11W + 13B = \frac{30080}{8} = 3760 \quad \text{---(Eq 2)} \]

• Solve the Linear System:
Multiply Eq 1 by 11 and Eq 2 by 3 to eliminate $W$:
\[ 33W + 44B = 11880 \quad \text{---(Eq 3)} \] \[ 33W + 39B = 11280 \quad \text{---(Eq 4)} \] Subtract Eq 4 from Eq 3:
\[ 5B = 600 \quad \implies \quad B = 120 \] Substitute $B = 120$ into Eq 1:
\[ 3W + 4(120) = 1080 \] \[ 3W + 480 = 1080 \] \[ 3W = 600 \quad \implies \quad W = 200 \] So, a woman earns Rs 200 daily, and a boy earns Rs 120 daily.

• Calculate Daily Earnings of the New Group:
The new group consists of 7 women and 9 boys.
Their combined daily earning is:
\[ \text{Daily Earning} = 7W + 9B = 7(200) + 9(120) = 1400 + 1080 = 2480 \text{ Rs/day} \]

• Calculate the Required Days:
To find the time needed to earn Rs 24800:
\[ \text{Number of days} = \frac{\text{Target earnings}}{\text{Daily earnings}} = \frac{24800}{2480} = 10 \text{ days} \]

Step 4: Final Answer:
The group of 7 women and 9 boys will earn the target amount in 10 days.
Therefore, the correct option is (C).