Question

If 10 men and 12 women can earn Rs.12880 in 7 days, and 15 men and 6 women can earn Rs.17280 in 9 days, then in how many days will 8 men and 10 women earn Rs.15000?

• A. 6 days
• B. 7 days
• C. 8 days
• D. 10 days

Answer 1

Answer:

D. 10 days

Solution: Let 1 men 1 day’s earning be Rs.’x’ and 1 women 1 day’s earning be Rs.’y’. Then, in 1 day, 10 men and 12 women will earn, ⇒ 10x + 12y = 12880/7 ⇒ 10x + 12y = 1840 Dividing by 2, ⇒ 5x + 6y = 920 - - - - - (1) Also, in 1 day, 15 men and 6 women will earn, ⇒ 15x + 6y = 17280/9 ⇒ 15x + 6y = 1920 Dividing by 3, ⇒ 5x + 2y = 640 - - - - - (2) Subtracting (2) from (1), 5x + 6y – 5x – 2y = 920 – 640 ⇒ 4y = 280 ⇒ y = 280/4 = Rs.70 Substituting in (1), 5x + 6(70) = 920 ⇒ x = 500/5 = Rs.100 Therefore, in 1 day, 8 men and 10 women will earn, ⇒ 8x + 10y = 8(100) + 10(70) = Rs.1500 Hence, to earn Rs.15000, 8 men and 10 women will take (15000/1500) = 10 days