Question

15.B can do a work 6 days lesser
than A. If A and B can do the
same work in 4 days, B can com-
plete the work in how many
days?

Answer 1

Answer:

B can complete the work in 6 days

Step-by-step explanation:

Let the number of days taken by A to complete the work = x

Then, the number of days taken by B to complete the work = x-6

If A takes "x" days to complete the work,

the fraction of work done by A in 1 day = 1/x  .......(i)

Similarly,

the fraction of work done by B in 1 day = 1/(x - 6)  .......(ii)

ATQ,

A and B together can complete the work in 4 days

=> A and B together can complete (1/4) work in 1 day

IF working together,

the fraction of work done by (A and B) = 1/4

From (i) and (ii), we get:

$\frac{1}{x} + \frac{1}{x-6} = \frac{1}{4}$

$\frac{x(x-6)+x}{x(x-6)} = \frac{1}{4}$

4(2x - 6) = x(x - 6)

8x - 24 = x² - 6x

x² - 14x + 24 = 0

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

=> x = 12 or x = 2

x = 2 is inadmissible as it would mean (x - 6) is negative. Now, (x - 6) is the number of days taken by B to complete the work. This cannot be negative.

Hence, x = 12

No. of days taken by A to complete the work = x = 12

No. of days taken by B to complete the work = (x-6) = 6