M, N and P were each paid the same hourly rate to paint a building. M worked for a full day, N worked for half a day and P worked half as long as N worked. Together they earned BDT 560. How much money did N receive?

Question: M, N and P were each paid the same hourly rate to paint a building. M worked for a full day, N worked for half a day and P worked half as long as N worked. Together they earned BDT 560. How much money did N receive?

Solution:
Let the full day worked by M be 1 unit.
M worked = 1 full day
∴ N worked = 1/2 of a day
∴ P worked = 1/2 of N = 1/2 × 1/2 = 1/4 of a day

Since they are paid the same hourly rate, the money is divided according to the time worked.
Let the total pay for a full day be x.
According to the question,
M's share + N's share + P's share = 560
⇒ x + x/2 + x/4 = 560
⇒ 4x + 2x + x = 560 × 4 [উভয়পক্ষে 4 দ্বারা গুণ করে]
⇒ 7x = 2,240
⇒ x = 2,240/7
∴ x = 320

Now, N's share = x/2
= 320/2
= 160
∴ N received BDT 160.

Correct Answer: খ) 160