Question

A can complete a certain piece of work in 40 days. B is 25% more efficient than A and C is 28% more efficient than B. They work together for 5 days. The remaining work will be completed by B alone, in:

Answer 1

The number of days B take alone to complete the remaining work is 32 days .

Step-by-step explanation:

Given as :

A can complete a certain piece of work in 40 days

B is 25% more efficient than A

C is 28% more efficient than B

The number of days all three works together = 5 days

Let The number of days B take alone to complete the work = d days

According to question

Ratio of efficiency by A and B = 125 : 100

i.e Ratio of efficiency taken by A and B = 5 : 4

Then ,

Ratio of efficiency taken by A and B = Ratio of days taken by A and B

i.e  5 : 4 = 40 : d

Or, $\dfrac{5}{4}$  = $\dfrac{40}{d}$

By cross multiplication

or,  5 ×  d = 4 × 40

Or,        d = $\dfrac{4\times 40}{5}$

∴           d = 32

So, The number of days B take alone to complete the work = d = 32 days

Similarly

Ratio of efficiency taken by C and B = 128 : 100

i.e Ratio of efficiency taken by C and B = 32 : 25

Ratio of efficiency taken by C and B = Ratio of days taken by C and B

Let number of days C take alone = D days

i.e  32 : 25 = D : 32

Or, $\dfrac{32}{25}$  = $\dfrac{D}{32}$

By cross multiplication

or,  32 ×  32 = D × 25

Or,        D = $\dfrac{32\times 32}{25}$

∴           D = 40 $\dfrac{24}{25}$

So, The number of days C take alone to complete the work = D  = 40 $\dfrac{24}{25}$ days

Hence,  The number of days B take alone to complete the remaining work is 32 days . Answer

Answer 2

A can complete a certain piece of work in 40 days. B is 25% more efficient than A and C is 28% more efficient than B. They work together for 5 days. The remaining work will be completed by b alone,in: 32 days

Stepwise explanation is given below:

It is given that the-

- A can complete a certain piece of work in 40 days.

B is 25% more efficient than A

C is 28% more efficient than B

- The number of days all three works together = 5 days.

- The number of days B take alone to complete the work = d days

- Acc. to the question

Ratio of efficiency by A and B = 125 : 100

i.e Ratio of efficiency taken by A and B = 5 : 4

- Ratio of efficiency taken by A and B = Ratio of days taken by A and B

i.e  5 : 4 = 40 : d

Or, (5/4) = (40/d)

- By cross multiplication

 5 ×  d = 4 × 40

5d = 4 × 40

d= (4 × 40)/5

d= 32

- So, The number of days B take alone to complete the work = d = 32 days.