Question

A can do a piece of work in 20 days whereas B can do it in 30 days both of them start the work together and work for sometime then B leaves if a completes the remaining work in 10 days then find the number of days for which they work together

Answer 1

Given :-

• A can do a piece of work in 20 days.
• B can do it in 30 days.
• Both Started Together.
• B left.
• A completes the remaining work in 10 days.

To Find :-

• The number of days for which they work together ?

Solution :- (By LCM Method).

LCM of 20 & 30 = 60unit = Let Total work.

So,

→ A alone can complete Total work in = 20 days .

→ Efficiency of A = (Total work) / No. of days = 60/20 = 3 unit/ day.

Similarly,

→ B alone can complete Total work in = 30 days .

→ Efficiency of A = (Total work) / No. of days = 60/30 = 2 unit/ day.

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Now, it is given that, in last 10 days A alone did the work.

So,

→ in Last 10 days A did = 10 * 3 = 30 unit of work.

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So, we can say That, rest work was done by Both of them , when they were together ,

Therefore,

→ left work = 60 - 30 = 30 unit.

→ Efficiency of A + B = 3 + 2 = 5 unit / day.

→ Time taken By them = (30/5) = 6 days. (Ans.)

Hence, A & B work together for 6 days.

Answer 2

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$\huge\tt{GIVEN:}$

• A can do a piece of work in 20 days whereas B can do it in 30 days both of them start the work together and work for sometime then B leaves if a completes the remaining work in 10 days

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$\huge\tt{TO~FIND:}$

• The number of days for which they work together

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$\huge\tt{SOLUTION:}$

As we know, the LCM of 30 & 20 is 60, Let 60 be the unit of work done

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➠A can do the Total work in = 20 days

➠Efficiency of A = (Total work) / No. of days = 60/20 = 3 unit/ day

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➠B can do The Total work in = 30 days

➠ Efficiency of A = (Total work) / No. of days = 60/30 = 2 unit/ day

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Now, we know that A did work alone for 10 days...

So,

In last 10 days ,A did 30 units of work

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We know than the rest of the work was done by both of 'em

Then,

The remaining work = (60-30) = 30 units of work

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➠Efficiency of A + B = 3 + 2 = 5 unit/day

➠Work done by them = 30÷5 = 6 Days

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$\tt{WORK~DONE~BY~THEM~TOGETHER=6~DAYS}$

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