Aptitude - Time and Work - Discussion

Friends, don't make it complex: Here we go.

Ratio of time taken by A & B = 1:3

And A takes 60 days less then B

Suppose, days taken by B = x then days taken by A = (x - 60)

Thus,

A : B = (x - 60) : x
1 : 3 = (x - 60) : x
1/3 = (x - 60) / x
X = 3 (x - 60)
X = 3x - 180
180 = 3x - x
180 = 2x
X = 180 / 2 = 90

Hence,
Days taken by B = x = 90 days
Days taken by A = (x - 60) = 90 - 60 = 30 days

1 day work of A and B = 1/30 + 1/90
= 4/90
= 2/45

So,
Total days taken by A & B to complete the work = 45/2 = 22.5 days

Formula-->nx- (n+1) /nx.
4x-4x/3=60 so x=45/2.

So by the explanation above we have to take in the ratio 1:3.

A is twice as good a workmen as B and together they can finish a piece of work in 18days. In how many days will A alone finish the work?

Can we solve the above problem using the formula k*x/k^2-1.

Let A takes x days to do the work alone
Therefore days taken by b is (x+60).

Now A is 3 times faster than B
So no.of days taken by A will be 3 times less than B.
So
3*x=(x+60)
2x=60
x=30 days //work done by A
Work done by B=30+60=90 days.

Now we can find work done together
1/30 +1/90 to get the answer.

We have a direct formula for these kind of questions .. i.e.,

Work done together is given by = (m*d)/(m^2 - 1),

Where d is no of days taken by B and m is no of time A is faster than B,
Therefore = (3*60)/(3^2-1) = 22.5.

@All.

Please refer to Sheetal's response as given below. Its the best and easiest way to solve such questions.

PS:Thanks sheetal.

"A is K times as good a worker as B & takes X days less than B to finish the work. Then the amount of time required by A & B working together is K * X / K'S SQUARE - 1.

SO IN QUESTION K IS 3. X IS 60. SO PUTTING THE VALUES IN ABOVE MENTIONED FORMULA.

K * X / K'S SQUARE - 1
=3 * 60 / 9 - 1
=3 * 60 / 8
=180 / 8
=22.5 DAYS.

AS MENTIONED OPTION B.

Simple way:

A and B ratio 1:3.

Since A finishes 60 days lesser than be A takes 90 days and B takes 30 days.

So per day calculation (1/90+1/30) = 22.5 days.

If A is thrice as good as workman B,
Than A=3B ----(1) or B=A/3 --------(2).

If A is finish a job in 60 days less than B.
Than A = B-60.

Put the value of B from Eq.(2).

A = A/3 -60
3A = A-180
2A = 180
than A = 90 Days.

Same Put the value of A in Eq.(2).
B=90/3 = 30 Days.

So Working together (A+B) = 1/90 + 1/30.

A+B = 2/45.
or A+B =45/2 = 22.5 or 22 1/2.

Answer.22 1/2 Days.

Simple yaar.

>A is thrice as good as workman as B and therefore is able to finish a job in 60 days=IF B TAKE 90 DAYS THEN A WILL TAKE 30 (60 DAYS LESS).

>1/30 (PLUS) 1/60=4/90==>90/4==>22. 5 SIMPLE.