Two men and three boys can do a piece of work in ten days; while three men and two boys can do the same work in eight days. In how many days can two men and one boy do the work?
Explanation
Correct Option - 1
2 men + 3 boys completed work in 10days.
3 men + 2 boys completed work in 8 days.
Formula Used:
m1.d1.t1.e1 = m2.d2.t2.e2
w1.c1 = w2.c2
m = number of total men, women, and boys, etc.
d = number of days required to complete a work
t = number of working hours in a day
e = efficiency of total men, women, and boys, etc.
w = total units of work
c = units of consumption
Calculation:
m1.d1.t1.e1 = m2.d2.t2.e2
w1.c1 = w2.c2
⇒ (2 men + 3 boys) × 10 = (3 men + 2 boys) × 8
⇒ 20 men + 30 boys = 24 men + 16 boys
⇒ 14 boys = 4 men
⇒ 7 boys = 2 men
Efficiency of 1 man and 1 boy is 7 and 2 respectively.
Now two men and one boy do the same work,
Let the number of days be x
⇒ (2 men + 3 boys) × 10 = (2 men + 1 boy ) × x days
⇒ 20 men + 30 boys = (2 men + 1 boy ) × x days
⇒ 20(7) + 30(2) = {2(7)+1(2)}× x days
⇒ 140 + 60 = (14 + 2)× x days
⇒ 200 = 16 × x days
⇒ x days = 200/16
⇒ x days = 12.5 days
∴ 2 men and 1 boy will complete the same work in 12.5 days.
