-
4 men and 6 woman get ₹ 1600 by doing a piece of work in 5 days. 3 men and 7 women get ₹ 1740 by doing the same work in 6 days. In how many days, 7 men and 6 women can complete the same work getting ₹ 3760?
-
- 6 days
- 8 days
- 10 days
- 12 days
Correct Option: B
∵ In 5 days , (4 men + 6 women ) get ₹ 1600.
∴ In 1 day, (4 men + 6 women) get ₹ 1600/5 = ₹ 320 ....(i)
In 1 day number of person to get ₹ 1 = 320 / 4 men + 6 women ....(ii)
Similarly, in second condition,
In 1 day, number of person to get ₹ 1 = (1740 / 6) x (3 men + 7 women)
= 290 / (3 men + 7 women) ....(iii)
From Eqs. (ii) and (iii), we get
320 / (4 men + 6 women) = 290 / (3 men + 7 women)
96 men + 224 women = 116 men + 174 women
⇒ 20 men = 50 women
⇒ Man / Women = 5/2
∴ 1 women = 2/5 man
From Eq. (i), 1 day,
(4 men + 6 women) = (4 men + 6 x 2/5 men) = 32/5 men get ₹ 320
∴ In 1 day, 1 man get = 320 x 5 /32 = ₹ 50
∴ In 1 day, 1 woman get = 50 x 2/5 = ₹ 20
∴ In 1 day, (7 men + 6 women) get
7 x 50 + 6 x 20 = ₹ 470
∴ Required number of days = 3760 / 470 = 8 days
