JAMB 2020 Mathematics · Question 26

Four boys and ten girls can cut a field first in 5 hours. If the boys work at 5/4 the rate at which the girls…

Question

Four boys and ten girls can cut a field first in 5 hours. If the boys work at $\frac{5}{4}$ the rate at which the girls work, how many boys will be needed to cut the field in 3 hours?

A.180
B.60
C.25
D.20

Answer: D. 20

Explanation written with AI and checked against the answer key

Analyze the question: The problem is about work rate. A group of 4 boys and 10 girls finishes the field in 5 hours. Boys work at 5/4 the rate of girls. We need to find how many boys alone would be needed to cut the field in 3 hours. Concept: Work = rate × time. If the total work is 1 field, the combined rate is 1/(time). Solution: Let the girl's rate be g (fields per hour). Then a boy's rate is (5/4)g. Combined rate of 4 boys and 10 girls: 4 × (5/4)g + 10g = 5g + 10g = 15g They finish in 5 hours, so: 15g × 5 = 1, so g = 1/75 Boy's rate = (5/4)(1/75) = 1/60 field per hour. To cut the field in 3 hours, we need a rate of 1/3 field per hour. Number of boys = (1/3) ÷ (1/60) = 20 Check: 20 boys × (1/60) × 3 hours = 1 field. ✓ Answer: 20 boys, which is option D. Tip: Convert everything into one unit, such as "girl-units" or "boy-units". Here 4 boys + 10 girls = 15 girl-units; 15 girl-units for 5 hours = 75 girl-hours of work. In boy-units, 75 girl-hours = 60 boy-hours. For 3 hours you need 60 ÷ 3 = 20 boys.

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