Aptitude - Time and Work - Discussion

It is 7/10

1/15+1/20 LCM of this is 60.
So,
(1/15 * 60 + 1/20 * 60)/60we can simplify this you can get (4+3)/60 = 7/60.

@L Raj Scope

Please understand this concept first.

LET CONSIDER A SIMPLE STATEMENT:

A can do a work in 2 days.

That means A's 1 day work = 1/2.

This is the methodology we wanna apply on the data which is given in question.

From the question.

A (CAN D0 A JOB) ----15 days.
B (CAN DO A JOB) ----20 days.

Therefore by the above concept A's 1 day work = 1/15.

B's 1 day work = 1/20.

Therefore both A&B 1 work = (1/15)+1/20) = 7/60.

NOW READ THE QUESTION.

If A&B work together for 4 days then what the fraction of work left.

Consider:

Total work = 1.

A&B (4 DAYS WORK) = (7/60)*4 = 7/15.

REMAIN B WORK = (TOTAL WORK)-(COMPLETED WORK BY A&B FOR 4 DAYS).

= 1-7/15.

= 8/15.

Hope this is helpful.

LCM of A's and B's:
A-15
B-20.

LCM is 60 (It is also total Work) and Efficiency is TOTAL WORK/ TIME i.e.
60/15 = 4 <<<A's 1 day Efficiency
60/20 = 3 <<<B's 1 day Efficiency.

Combining both 1-day Efficiency then we get 4+3=7 (It means A and B can do 7 units in 1 day)

According to the question:
if they have 7 unit Efficiency they work for 4 days then we get:

7 x 4 and divide by total work (60).
7 x 4/60= 7/15 << it is the part of work they will finish in 4 days.

But the question was asked about how much fraction is left then simply we know that total work is 1 then subtract total work 1-7/15.

We get 8/15 that is the answer.

How 1-7/15? Explain.

I am not getting. How 1-7/15? Explain, please.

Thanks everyone for explaining the answer.

(+1-7/15).
(-*-=+) = 8/15.

Can you explain how 7/60 came?

When dealing with addition or subtraction of fractions you consider the denominators i.e
15&20 and then you find the L.C.M which is 60 or multiply them together.

15*20 = 300 so,

(1/15 + 1/20)/300 = (20 + 15)/300.

=25/300 reduce to the lowest term and you get 7/60.

This 7/60 is the amount of work A & B will complete in one day.
Hence for 4 days we have;

7/60 * 4 = 7/15 of the total work.

Since we don't know the real value of the total work we then assume total work to be done to be 1.

Therefore,

Remaining work left will be,

1- (work done)

1-7/15 ; the denominator here is 15 & 1 (since 1 =1/1).

Do the math and you get our final answer to be 8/15.

NOTE !

If you are subtracting a fraction from a whole number, just multiply the denominator by the whole number and then subtract from the numerator. The same rule applies for addition.