5 boys and 5 girls earn Rs. 660 in 3 days. 10 boys and 20 girls earn Rs. 3500 in 5 days. In how many days can 6 boys and 4 girls earn Rs. 1060?

A 5 days

B 10 days

C 6 days

D 12 days

E None of these

Correct Answer: Option A

Let amount of money earned by boys and girls in 1 day = ‘a’ and ‘b’ respectively,

Then,

⇒ 3 × (5a+ 5b) = 660

⇒ 5a + 5b = 220

⇒ a + b = 44 -----------[1]

Now,

⇒ 5 × (10a + 20b) = 3500

⇒ 10a + 20b = 700

⇒ a + 2b= 70 ------------[2]

Solving equations [1] & [2] we get,

⇒ b = 26 and a = 18.

Now let number of days 6 boys and 4 girls are made to work = N days,

Then,

⇒ N × (6 × 18 + 4 ×26) = 1060

⇒ N × (108 + 104) = 1060

⇒ N × 212 = 1060

⇒ N = 5 days.

Hence, 6 boys and 4 girls can earn 1060 rupees in 5 days.