Question

Four persons started to do a work together. 'A' works only in starting two days after that B, C and D works alternately starting from B. Ratio of time taken by A, B, C and Dif they work alone is 4: 3: 2: 5. If the work is completed in 12 days then in how many days A and Ccan complete the work if they work together?​

Answer 1

Given :

Four person A,B,C and D

All work together for first two days.

A stop working after two days.

B,C and D started working alternatively after 2 days started with B.

Ratio of time taken by A, B,C and D are respectively

4:3:2:5

Work completed in 12 days.

To find :

Days taken in completing the work when only A and C do work together.

Solution:

Ratio of time = 4:3:2:5

It means

In one day

$A \: \: do \: \frac{1}{4x} \: work \\ B \: \:do \: \: \frac{1}{3x} \: work \\ C \: \: do \: \: \frac{1}{2x} \: work \\ D \: \: do \: \: \frac{1}{5x} \: work$

(equation 1)

As it is given that

• A do work on first and second day only (total 2 days)
• B do work on 1,2,3,6,9 and 12th day (total 6 days)
• C do work on 1,2,4,7 and 10th day (total 5 days)
• D do work on 1,2,5,8 and 11th day (total 5 days)

Because of all the worl done by them, a work is fully completed.

It means

$(2 \times \frac{1}{4x} ) + (6 \times \frac{1}{3x} )+ (5 \times \frac{1}{2x} ) + (5 \times \frac{1}{5x} ) = 1$

so

$( \frac{2}{4x} ) + ( \frac{6}{3x} )+ ( \frac{5}{2x} ) + ( \frac{5}{5x} ) = 1 \\ \\ ( \frac{1}{2x} ) + ( \frac{2}{x} )+ ( \frac{5}{2x} ) + ( \frac{1}{x} ) = 1 \\ \\ ( \frac{1}{2x} ) + ( \frac{4}{2x} )+ ( \frac{5}{2x} ) + ( \frac{2}{2x} ) = 1$

So

$\frac{1 + 4 + 5 + 2}{2x} = 1$

multiplying both sides by 2x, we get

2x =12

So x = 6

It means in one day (putting value of x in equation 1)

$A \: \: do \: \frac{1}{24} \: work \\ B \: \:do \: \: \frac{1}{18} \: work \\ C \: \: do \: \: \frac{1}{12} \: work \\ D \: \: do \: \: \frac{1}{30} \: work$

If A and C do work together

So work done by both in 1 day :

$\frac{1}{24} + \frac{1}{12} = \frac{3}{24} = \frac{1}{8} = 0.125$

So Days taken by A and C together to do work :

$\frac{1}{0.125} = 8$

So

A and C together will do work in 8 days.