A, B and C can do a piece of work in 12, 15 and 24 days respectively. All three started working together and C left after working for p days. B left p days before the work got completed. If it took m days to complete the work and m, p are integers, find the value of m.

What I did

when there are two variables, I assume one value to be some value and then I solve

So Total work is 120

A=10 units

B=8 units

C=5 units

Let p=10

23(10)+18(m-20)+10(10)=120

m came out as 50/6

but ans is 7

where I am wrong @TanujA3 @khan.moin00103

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Solutions and approach please.

P is 2 and m is 7. You can't assume that p is 10. Suppose total units are120 units. A works for the entire m days, so, 10m units, B works for (m-p) days, hence 8(m-p) units and C works for initial p days, hence, 5p units. Total is 10m + 8(m-p) + 5p = 120. Relation comes as 6m = p+40. Only one pair of values of (p,m) will satisfy this, i.e. (2,7). Answer = 7.