Question

9 men and 12 boys finish a job in 12 days,12 men and 12 boys finish it in 10 days. 10 men and 10 boys shall finish it in how many days

Answer 1

9M + 12B ----- 12 days ...........(1)
12M + 12B ------- 10 days........(2)
10M + 10B -------?
108M + 144B = 120M +120B
24B = 12M => 1M = 2B............(3)

From (1) & (3)

18B + 12B = 30B ---- 12 days

20B + 10B = 30B -----? => 12 days.

Answer 2

Answer: 10 men and 10 boys can finish the same work in 12 days.

Step-by-step explanation:

Since we have given that

9 men and 12 boys finish a job = 12 days

12 men and 12 boys finish a job = 10 days

We will use "Time and work ":

$(9M+12B)\times 12=(12M+12B)\times 10\\\\108M+144B=120M+120B\\\\144B-120B=120M-108M\\\\24B=12M\\\\M=2B$

We need to find the number of days in which 10 men and 10 boys can finish the same work.

$(10M+10B)\times x=(9M+12B)\times 12\\\\(20B+10B)\times x=(18B+12B)\times 12\\\\30B\times x=30B\times 12\\\\x=12$

Hence, 10 men and 10 boys can finish the same work in 12 days.