Question

Pintu takes 6days more than nishu to complete certain work. If they work together they finish in 4days. How many days it will they work alone

Answer 1

Solution:-

Let x be the Number of days to complete work by Nishu.

Work done in 1 day by Nishu = 1/x days

=> Pintu takes x + 6 days.

=> Work done by Pintu in 1 day = 1/ x+6

A.T.Q.

$= > \frac{1}{x} + \frac{1}{x + 6} = \frac{1}{4} \\ \\ = > \frac{x + 6 + x}{x(x + 6)} = \frac{1}{4} \\ \\ = > 8x + 24 = {x}^{2} + 6x \\ \\ = > {x}^{2} + 6x - 8x - 24 = 0 \\ \\ = > {x}^{2} - 2x - 24 = 0 \\ \\ = > {x}^{2} - (6 - 4)x - 24 = 0 \\ \\ = > {x}^{2} - 6x + 4x - 24 = 0 \\ \\ = > x(x - 6) + 4(x - 6) = 0 \\ \\ = > (x - 6)(x + 4) = 0 \\ \\ = > x = 6 \: \: \: and \: \: \: x = - 4(neglect).$

Hence,

Number of Days taken by Nishu to complete the work = 6 days.


Number of Days taken by Pintu to complete the work = 12 days.

Answer 2

⭐⭐ heya mate ⭐⭐

Let Pintu take = x days

Nishu takes = (x - 6) days

In one day

Pintu does = 1/x

Nishu does = 1/(x - 6)

The two together do 1/x  + 1(x - 6), and they take 4 days;

So

1/x  + 1(x - 6) = 1/4 

8x - 24 = x² - 6x

x² -14 + 24 = 0

x² - 2x - 12x + 24 = 0

x(x - 2) - 12(x - 2) = 0

(x - 12)(x - 2) = 0

Either

x - 12 = 0

x = 12

or

x - 2 = 0

x = 2

x can not be 2, so we take x = 12

Pintu alone takes = 12 days

Nishu alone takes = 12  - 6  = 6 days

hope it helps you....

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