Question

.  A alone can finish a work in X days. B alone can finish the same work in X+5 days. Together, they take 6 days to complete the work. Find X.
​

Answer 1

Answer:

x=10

Step-by-step explanation:

A alone can do in 1/x days

B alone can do in 1/(x+5) days

both together can do in

1/x+1/(x+5)=1/6

2x+5/x(x+5)=1/6

x^2-7x-30

by solving x =10,-3 ignore negative

Answer 2

Answer:

10 is the required value of X

Step-by-step explanation:

Explanation:

Given , A alone can finish a work in X days

B alone can finish the same  work  in (X+5 )days

and A and B together finish the same work in 6 days .

Step1:

A's 1 day work = $\frac{1}{X}$

B's 1 day work = $\frac{1}{X+5}$

and (A + B)'s  1 day work = $\frac{1}{6}$

Therefore ,

$\frac{1}{X}+ \frac{1}{X+5} = \frac{1}{6}$

⇒$\frac{(X+5)+X}{X(X+5)} = \frac{1}{6}$

⇒$\frac{2X+5}{X(X+5)} = \frac{1}{6}$ ⇒6(2X+5) = X(X+5)       (by cross multiplication)

⇒$12X +30 =$$X^{2} +5X$

⇒$X^{2} -7X -30 = 0$

After factorization the above equation we get ,

(X-10)(X-3)=0⇒ X = 10 , -3   (-3  which is negative sign so w take x=  10 )

Final answer :

Hence , the value of X is 10 .