If 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is:

Explanation

We are given:

• 12 men + 16 boys complete the work in 5 days

• 13 men + 24 boys complete the work in 4 days

• We need to find the ratio of the daily work done by a man to that of a boy.

Step 1: Let M be work done by 1 man in 1 day and B be work done by 1 boy in 1 day

5(12M+16B)=1

4(13M+24B)=1

Step 2: Convert to equations

12M+16B=⅕

4(13M + 24B) = 1​

Step 3: Solve for M and B

Multiply first equation by 4:

48M+64B=⅘

Multiply second equation by 5:

65M+120B=5/4

Convert fractions:

4/5=0.8,5/4=1.25

Solving simultaneously:

Using elimination: Multiply (48M + 64B = 0.8) by 5:

240M+320B=4240M + 320B = 4240M+320B=4

Multiply (65M + 120B = 1.25) by 4:

(260M+480B)- (240M + 320B) =5-4

20M + 160 b = 1

Dividing by 20:

M+8B=1/20M 

Substituting M = 2B from Question 69:

2B+8B=1/20

10B=20/1​

 B=1/200B

​ M=2×1/200=2/200=1/100M

Thus, ratio M:B = 2:1.

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