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:
Answer: 2 : 1
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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