Question

If 3 men and 4 boys together earn rs. 264 in 8 days and 2 men and 3 boys together earn rs. 184 in the same time, then in how many days will 6 men and 7 boys together earn rs. 315 ?

Answer 1

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Answer 2

They will earn Rs. 315 in 5 days.

Step-by-step explanation:

Let one man can earn in one day Rs. x and one boy can earn in one day Rs. y.

Given that 3 men and 4 boys together earn Rs. 264 in 8 days.

Therefore, 8(3x + 4y ) = 264

⇒ 3x + 4y = 33 ......... (1)

⇒ 6x + 8y = 66 ........ (2)

Again, 2 men and 3 boys together earn Rs. 184 in the same time i.e. 8 days.

Hence, 8(2x + 3y) = 184

⇒ 2x + 3y = 23 ........... (3)

⇒ 6x + 9y = 69 ........... (4)

Now, solving equations (2) and (4) we get,

9y - 8y = 69 - 66 = 3

⇒ y = 3 Rs.

Now, from equation (1) we get

3x = 33 - 4(3) = 21

⇒ x = 7 Rs.

Therefore, 6 men and 7 boys together can earn in one day is (6 × 7 + 7 × 3) = 63 Rs.

So, they will earn Rs. 315 in $\frac{315}{63} = 5$ days. (Answer)