Question

A, b, c and d can do a piece of work in 40 days. if a and b can do it together in 100 days, and c alone in 120 days, find the time in which d alone can do it.

Answer 1

Consider the time required by A to finish the work be a days, similarly for others B in b days, C in c days, D in d days.

Work done by each in one day
A= 1/a
B= 1/b
C= 1/c
D = 1/d

If they all work together, the amount of work done in one day is 1/40,
if A and B work together then 1/100,
if C alone then 1/120

thus: 1/a + 1/b +1/c 1/d = 1/40
1/a +1/b =1/100
1/c = 1/120

By substituting the values you can calculate for D

Answer 2

The time taken by d to complete the work alone is 150 days.

Given,

a,b,c, and d do a piece of work in 40 days.

a and b together complete work in 100 days.

c alone completed the work in 120 days.

To Find,

the time in which d alone can complete the work.

Solution,

a+b+c+d=40 days

a+b=100days

c=120

let's take the L.C.M of the 40,100 and 120

LCM of 100, 120 and 40 = 600

so,

a+b+c+d=$\frac{600}{40\\}$= 15 unit / day.

a+b=$\frac{600}{100}$= 6 unit / day.

c=$\frac{600}{120}$= 5 unit / day.

then,

a+b+c+d= 15 unit / day

on putting values of a+b and c in the above

6+5+d=15

d= 15-11

d=4 unit / day.

so,

d=$\frac{600}{4}$

d= 150 days.

The time taken by d to complete the work alone is 150 days.

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