5 men and 7 women can earn Rs. 6440 in 7 days. 15 men and 17 women can earn Rs. 20160 in 8 days. In what time, will 21 men and 29 women earn Rs. 65280?

A 15 days

B 16 days

C 17 days

D 18 days

E None of these

Correct Answer: Option C

Let the amount earned per day by a man and a woman be ‘x’ and ‘y’ respectively.

Amount earned by 5 men and 7 women in 7 days = (5x + 7y) × 7 = Rs.6440

⇒ 5x + 7y = 6440/7 = 920 …. (1)

Amount earned by 15 men and 17 women in 8 days = (15x + 17y) × 8 = Rs.20160

⇒ 15x + 17y = 20160/8 = 2520 …. (2)

Solving (1) and (2)

We get,

x = Rs. 100 and y = Rs. 60

Amount earned by 21 men and 29 women in one day = 21x + 29y = 21 × 100 + 29 × 60 = Rs.3840

Time taken by 21 men and 29 women to earn Rs.65280 = 65280/3840 = 17 days