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Charlie and Lola together can do a piece of work in 20 days. They worked for 15 days, then Lola left the work. Charlie finished the remaining work in 12 days. Find in how many days Charlie alone can complete the work?

Charlie and Lola together can do a piece of work in 20 days. They worked for 15 days, then Lola left the work. Charlie finished the remaining work in 12 days. Find in how many days Charlie alone can complete the work? Correct Answer 48

Given:

Charlie and Lola together can do a piece of work in 20 days.

They worked for 15 days, then Lola left the work.

Charlie finished the remaining work in 12 days.

Concept used:

Entire work = Work Done Each Day × Total Time Taken

Calculation:

Let's consider the entire work to be 100%.

So, Charlie and Lola together do = (100 ÷ 20)% = 5% each day

Hence, in 15 days, completed work = 15 × 5% = 75%

Now, remaining work = (100 - 75)% = 25%

So, Charlie does each day = (25/12)% of the work

Hence, time taken by Charlie to complete the work alone = 100% ÷ (25/12)% = 48 days

∴ Charlie alone can complete the work in 48 days.

Shortcut Trick Let's take the total work to be the LCM of 20,15,12.

So, the entire work = 60 units

Hence, Charlie & Lola do each day = 60 ÷ 20 = 3 units

In 15 days, work done = 15 × 3 =  45 units

Remaning work = 60 - 45 = 15 units

C does each day = 15 ÷ 12 = 5/4 units

Hence, time taken by C to complete the entire work alone = 60 ÷ (5/4) = 48 days

∴ Charlie alone can complete the work in 48 days.

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