Question

4. A takes half as long to do a piece of work as B
takes, and if C does it in the same time as A and
B together, and if all three working together would
take 7 days, how long would each take separately
(a) 21 days, 42 days, 14 days
(b) 20 days, 40 days, 40/3 days
(c) 15 days. 45 days, 45/4 days
(d) None of these​

Answer 1

Answer:

Let the time taken by A = t

—> Time taken by B = 2t &

Time taken by C = 2t*t/(2t + t) = 2t/3

working together they can complete 7 days

—> 1/t + 1/2t + 3/2t = 1/7

—> 3/t = 1/7

—> t = 21 days

A = t = 21

B = 2t = 42

C = 2t/3 = 2/3*21 = 14

Answer 2

Concept

A straightforward mathematical ratio of usable output to input may be used to quantify efficiency.

Given

A take half as long to do a piece of work as B

C does it same time as A and B together

Find

We need to find the time they will take to work saperately

Solution

Given that  A take half as long to do a piece of work as B

So , let the Ratio of A: B = 1:2

suppose the piece of work done by A is 1

Then obviously the piece of work done by B will be 2

We know that Efficiency is inversely proportional to time

Therefore

A = 2

B = 1

Now it is given that

A+B =C

2+1 = 3

Hence the amount of work done by C is 3

Now calculating the time that will be taken by each of them to work separately

Total Work done = 7 (3+2+1)

= 7 (6)

= 42

Now Time taken by A = 42 / 2 = 21 days

Time taken by B = 42/1 = 42 days

Time Taken by C = 42/3 = 14 days

Hence The Time taken will be 21 days , 42 days , 14 days

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