Question

Neha can do a work in 2 days while Megha can do the same work in 3 days. Both of them finish the work together and get Rs 450. The share (in Rs) of Neha is :

• A. 270
• B. 352
• C. 426
• D. 480

Hint:

For two workers, the wage ratio is simply the reverse of their time ratio:
Since Neha and Megha take $2$ and $3$ days, their wages must be divided in the ratio $3 : 2$.
Since Neha is faster, she gets the larger portion of the Rs 450 (i.e., more than half).
This immediately eliminates options B, C, and D, which are either incorrect or exceed the total budget of Rs 450!

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question relates to the distribution of wages among workers based on their rates of work.
When multiple people work together to complete a task, their wages are distributed in the ratio of the amount of work each person does.
Since they work together for the same duration, the work done by each is directly proportional to their individual efficiencies (work rates).

Step 2: Key Formula or Approach:
The rate of work of a person is inversely proportional to the time they take to complete the work alone.
If Neha takes $T_N$ days and Megha takes $T_M$ days, the ratio of their efficiencies is:
\[ E_N : E_M = \frac{1}{T_N} : \frac{1}{T_M} = T_M : T_N \] Wages are distributed in this efficiency ratio.

Step 3: Detailed Explanation:

• Identify Individual Time and Efficiency:
- Time taken by Neha ($T_N$) $= 2 \text{ days}$.
- Time taken by Megha ($T_M$) $= 3 \text{ days}$.
The ratio of their work rates (efficiencies) is:
\[ \text{Neha's Rate} : \text{Megha's Rate} = \frac{1}{2} : \frac{1}{3} \] Multiply by $6$ to get integer ratios:
\[ \text{Ratio} = 3 : 2 \]

• Distribute the Total Wages:
The total wages earned together is Rs 450.
The sum of the ratio parts is $3 + 2 = 5$ parts.
Neha's share of the wages corresponds to $3$ out of these $5$ parts:
\[ \text{Neha's Share} = 450 \times \frac{3}{5} \] \[ \text{Neha's Share} = 90 \times 3 = 270 \text{ Rs} \]

Step 4: Final Answer:
The share of Neha is Rs 270.
Thus, the correct option is (A).