Question

X working alone takes 75 days more than Y to do a work, and working together they complete 12 de
If a certain sum has been earmarked as wages for this work in what ratio should it get distributed ang
and Y?​

Answer 1

Given :- X working alone takes 75 days more than Y to do a work, and working together they complete 20 days. If a certain sum has been earmarked as wages for this work, in what ratio should it get distributed among X

and Y ?

Solution :-

Let us assume that, Y alone can complete the work alone in x days.

Than, X will complete the work alone in (x + 75) days.

given that, both takes 12 days to complete the work .

So,

→ 1/x + 1/(x + 75) = 1/20

→ (x + 75 + x)/x(x + 75) = 1/20

→ (2x + 75) * 20 = x² + 75x

→ 40x + 1500 = x² + 75x

→ x² + 75x - 40x - 1500 = 0

→ x² + 35x - 1500 = 0

→ x² + 60x - 25x - 1500 = 0

→ x(x + 60) - 25(x + 60) = 0

→ (x + 60)(x - 25) = 0

putting both equal to zero , we get,

→ x = (-60) or 25.

since days cant be in negative.

Therefore,

→ Time taken by Y alone = 25 days.

→ Time taken by X alone = 25 + 75 = 100 days.

Now, we know that,

• Efficiency is indirectly proportional to time..
• wages is distributed among works in ratio of their efficiency of work per day.

So,

→ Time taken by X : Time taken by Y = 100 : 25 = 4 : 1 .

Than,

→ Efficiency of X : Efficiency of Y = 1 : 4.

Hence,

→ wages of X : wages of Y = 1 : 4 (Ans.)

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