X is 3 times as fast as Y and is able to complete the work in 40 days

1.	X is 3 times as fast as Y and is able to complete the work in 40 days less than Y. Then the time in which they can complete the work together is1). 15 days2). 10 days3). \(7\frac{1}{2}days\)4). 5 days
Answer» Let X can complete the work alone in X’ days then according to question: Time taken by Y to complete the work alone = 3X’ Given, X can complete the work in 40 days less than Y. Then, ⇒ X’ = 3X’ – 40 ⇒ X’ = 20 Thus, X can complete the work alone in 20days while Y can do it alone in 60 days. Let the total work be denoted by W units. Then, PORTION of work done by X alone in 1 day = W/20 Also, portion of work done by Y alone in 1 day = W/60 Let them together complete the work in D days. Then, $(\RIGHTARROW \LEFT( {\frac{W}{{20}} + \frac{W}{{60}}} \right) \times D = W)$ ⇒ D = 15 days Hence X and Y both can complete work in 15 days.

X is 3 times as fast as Y and is able to complete the work in 40 days less than Y. Then the time in which they can complete the work together is1). 15 days2). 10 days3). $7\frac{1}{2}days$4). 5 days

Answer»

Let X can complete the work alone in X’ days then according to question:

Time taken by Y to complete the work alone = 3X’

Given,

X can complete the work in 40 days less than Y. Then,

⇒ X’ = 3X’ – 40

⇒ X’ = 20

Thus, X can complete the work alone in 20days while Y can do it alone in 60 days.

Let the total work be denoted by W units. Then,

PORTION of work done by X alone in 1 day

= W/20

Also, portion of work done by Y alone in 1 day

= W/60

Let them together complete the work in D days. Then,

$(\RIGHTARROW \LEFT( {\frac{W}{{20}} + \frac{W}{{60}}} \right) \times D = W)$

⇒ D = 15 days

Hence X and Y both can complete work in 15 days.

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