Given:

5 men(M) with 7 boys(B) can earn Rs. 4185 in 7 days

2 men(M) with 3 boys(B) can earn Rs. 1230 in 5 days.

Calculation:

If 5 men with 7 boys can earn Rs. 4185 in 7 days

In one day,

⇒ 5M + 7B = 4185/7

⇒ 5M + 7B = 597.85      ____(1)

If 2 men with 3 boys can earn Rs. 1230 in 5 days

In one day,

⇒ 2M + 3B = 1230/5

⇒ 2M + 3B = 246      ____(2)

To solve equation (1) & (2) we have to make either the number of men or number of boys equal.

Thus,

Multiply by 2 in equation (1) and multiply by 5 in equation (2)

⇒ 10M + 14B = 1195.7      ____(3)

⇒ 10M + 15B = 1230      ____(4)

Subtracting equation (3) from (4)

⇒ B = Rs. 34.3 per day

Substituting this in any of the equation (1) or (2) we can find the daily wage of 1 man.

Thus, solving equation (2)

⇒ 2M + 3 × 34.3 = 246

⇒ 2M = 246 – 102.9

⇒ M = Rs. 71.55 per day

Now, daily wage of 7M + 6B 

⇒ 7 × 71.55 + 6 × 34.3

⇒ 500.85 + 205.8

⇒ Rs. 706.65

Required number of days = 21189/706.65

⇒ 30 days (approx).

∴ Time will 7 men with 6 boys earn Rs. 21189 in 30 days.