Question

4 boys and 6 girls get Rs. 3200 by doing a piece of work in 5 days. 3 boys and 7 girls get Rs. 3480 by doing the same work in 6 days. In how many days, 7 boys and 6 girls can complete the same work getting Rs. 7520?

1. 8 days
2. 4 days
3. 16 days
4. 10 days
5. 5 days

Answer 1

Correct Answer - Option 1 : 8 days

Calculations:

In 5 days, 4 boys and 6 girls get = Rs. 3200

∴ in 1 day 4 boys and 6 girls gets = 3200/5

⇒Rs. 640

In 1 day, number of people to get

Re. 1 = 640/(4 boys + 6 girls)      ----(i)

Similarly, in second situation:

In 1 day, number of people to get

Re. 1 = 3480/6(3 boys + 7 girls)    

⇒ 580/(3 boys + 7 girls)      ----(ii)

∴ From eq (i) and (ii)

⇒ 640/(4 boys + 6 girls) = 580/(3 boys + 7 girls)

⇒ 96 boys + 224 girls = 116 boys + 174 girls

⇒ 20 boys = 50 girls

⇒ 2 boys = 5 girls

∴ boys/girls = 5/2

∴ 1 girl = 5/2 boys

∴ From Eq. (i)

In 1 day

(4 boys + 6 girls)

⇒ 4 boys + 6 × 2/5 boys

⇒ 4 + 12/5 boys

⇒ 32/5 boys get Rs. 640

∴ in 1 day, 1 boy gets = 640 × 5/32

⇒ Rs. 100

∴ in 1 day, 1 girl gets = 100 × 2/5

⇒ Rs. 40

∴ in 1 day, (7 boys + 6 girls) get

⇒ (7 × 100 + 6 × 40)

⇒ (700 + 240)

Rs. 940

∴ Required number of days = 7520/940

⇒ 8 days

7 boys and 6 girls can complete the same work in 8 days.