Question

A and B together can complete the work in 35 days. If A works alone and completes 4/ 7 of that work and leaves the remaining work for B, thus if it takes 114 days to complete the work. So how many days will A, who is more proficient in both, take to complete all the work alone? ​

Answer 1

Step-by-step explanation:

Let tw=35

A+B)*35=35

A+B=1

B=1-A

A=35*4/7=20

20/A+15/B=114

Solving

114A^2-119A+20=0

A=95/114=5/6

T=35*6/5=42 days✓✓

Answer 2

Answer:

Time taken by A alone to complete work by herself is 42 days.

Step-by-step explanation:

Given:

• A and B together can complete the work in 35 days
• A works alone and completes 4/ 7 of that work.
• Total days to complete work is 114 days

To find: Time taken by A alone to complete the work

Solution:

Let the total amount of work be  35 units.

If A and B work together, then both of them complete their work 35/35 = 1 unit of work every day

Now let us take,

Let the amount of work done by A by herself in one day be X units

The amount of work done by B by herself in one day be y units.

Therefore,

x + y = 1

If A alone and completes 4/7 th of the task, then work done by A is $\frac{4}{7}$ × 35 = 20 units

Time taken by A to complete this 20 units of work =  $\frac{20}{x }$ days

If B alone and completes 3/7 th of the task, then work done by B  is $\frac{3}{7}$ × 35 = 15 units

Time taken by B to complete this 15 units of work =  $\frac{15}{y}$ days

Total time taken = 114 days

$\frac{20}{x} + \frac{15}{y} = 114$

15x + 20y = 114xy

x+y =1

y = x - 1

15 x + 20(1-x) = 114x(1-x)

15x + 20 - 20 x = 114x -114$x^{2}$

15x - 20x  -114x + 114$x^{2}$ +20

114$x^{2}$  -119x +20 = 0

Use factorizing method

114$x^{2}$  -24x - 95x +20 = 0

6x(19x - 4) - 5(19x - 4) = 0

(6x -5)(9x - 4) = 0

6x-5  = 0

6x = 5

x = 5/6

9x-4 = 0

9x = 4

x = 4/9

Therefore,

x = 5/6 ( Because A is more proficient than B)

Time taken by A alone to complete work by herself = $\frac{35}{\frac{5}{6} }$

                                                                           = 35 × $\frac{6}{5}$

                                                                           = 7 × 6

                                                                           = 42 days

Final answer:

Time taken by A alone to complete work by herself is 42 days.

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