Question

A and B can complete a certain task in 45 days and 60 days, respectively. Both worked together for 15 days.
then B left. The remaining task was completed by A and C together in next 7
7 days
. In how many days can
Calone do 50% of the same task is 40​

Answer 1

Given :- A and B can complete a certain task in 45 days and 60 days, respectively. Both worked together for 15 days ,then B left. The remaining task was completed by A and C together in next 7(1/2) days. In how many days can C alone do 50% of the same task ?

Solution :-

LCM of 45 and 60 = 180 units = Let Total work.

So,

→ Efficiency of A = (Total work) / (No. of day required to complete the work alone) = 180 / 45 = 4 unit / day.

similarly,

→ Efficiency of B = (Total work) / (No. of day required to complete the work alone) = 180 / 60 = 3 unit / day.

then,

→ in 15 days both completes = 15 * (4 + 3) = 15 * 7 = 105 unit of work.

So,

→ Left work to be done now = 180 - 105 = 75 units.

given that, left work was done by A and C in next 7(1/2) days.

Let us assume that, Efficiency of C is x unit/day.

A/q,

→ (15/2)(A + C) = 75 units.

→ 15(4 + x) = 75 * 2

→ 15(4 + x) = 150

→ 4 + x = 10

→ x = 10 - 4

→ x = 6 unit / day.

Therefore,

→ C alone do 50% of total work in = (50% of 180) / Efficiency of C = 90 / 6 = 15 days. (Ans.)

Hence, C alone do 50% of the same task in 15 days.

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