A takes twice as much time as B or thrice as much time as C to finish a piece of work; working together they can finish the work in 2 days. In how many days B can do the work alone?

a)
12 days

b)
4 days

c)
8 days

d)
6 days

e)
None of these

Correct answer is option 'D'. Can you explain this answer?

Question

A takes twice as much time as B or thrice as much time as C to finish a piece of work; working together they can finish the work in 2 days. In how many days B can do the work alone?

a)
12 days
b)
4 days
c)
8 days
d)
6 days
e)
None of these

Correct answer is option 'D'. Can you explain this answer?

Answer

Let c can finish a piece of work in x days.then a will finish the work in 3x days and b will finish in 1.5x days adding 1 day work of all three we get 1/x+1/3x/1/1.5x= 1/2 we will get x=4 and finally b will finish work in 1.5 ×4 = 6days

Answer

Suppose A,B,C as x,x/2,x/3
to finish work

x+x/2+x/3=1/2
6/x=1/2
x=12
B = x/2 = 6

Answer

Lets assume that A completes the work in 'x' days.

B completes the same amount of work in 'x/2' days because A takes twice the time than B.

C completes the same amount of work in 'x/3' days because A takes thrice the time than C.

Now the work completed by A in one day is '1/x'.

Work completed by B in one day is '2/x'

Work completed by C in one day is '3/x'

All three together can complete the work in '2' days as given in the problem. So the work done by all three together in one day is '1/2'.

Hence the equation: '(1/x + 2/x + 3/x) = 1/2'.

Evaluating the above equation gives the value 'x=12' which is the number of days taken by A to complete the work.

As we know that number of days taken by B complete the work is 'x/2', we substitute the 'x' value.

Hence the evaluation '12/2' where 12 is the value of 'x'.

HENCE THE TIME REQUIRED BY B TO COMPLETE THE WORK IS 6 DAYS.

Answer

Given:
- A takes double as much time as B or thrice as much time as C to finish a piece of work.
- Working together they can finish the work in 2 days.
- B alone can do the work in x days.

To find:
- The number of days A alone and C alone can do the work.

Solution:
Let's assume that C can do the work in y days.
From the given information, we can form the following equations:
- A = 2B = 3C
- A + B + C = 1/2 (as they can finish the work in 2 days)

Substituting the value of A in terms of B and C in the second equation, we get:
2B + B/2 + C/3 = 1/2
Multiplying both sides by 6, we get:
12B + 3B + 2C = 3
15B + 2C = 3

Substituting the value of B in terms of x in the above equation, we get:
15/x + 2C = 3
2C = 3 - 15/x
C = (3x - 15)/2x

Substituting the value of C in terms of x in the equation A = 3C, we get:
A = 9(x-5)/2x

Therefore, the number of days A alone and C alone can do the work are:
- A alone can do the work in 9(x-5)/2x days
- C alone can do the work in (3x-15)/2x days

As B alone can do the work in x days, we can substitute the value of x in the above equations to find the answer.

Answer:
Therefore, the correct answer is option D, i.e., B alone can do the work in 6 days. A alone can do the work in 27 days, and C alone can do the work in 9 days.

Answer

Suppose A, B and C takes x, x/2, x/3 days respectively to finish the work.

⇒ 12/2 = 6 Days.

Similar Quant Doubts

A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in

A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in

Manoj takes twice as much time as Anjay and thrice as much as Vijay to finish a piece of work.Together they finish the work in 1 day. What is the time taken by Manoj to finish the work?

Top Courses for Quant

Suggested Free Tests

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company