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Directions: Study the following questions carefully and choose the right answer:
1
A is twice as good as B and together they finish a piece of work in 16 days. The number of days taken by A alone to finish the work is
» Explain it
D
Let's assume B takes 2x days

∴   A will take x days. Applying the shortcut approach,

Total time taken by A & B

xy
x + y

Where, x is the time taken by A alone And y is the total time taken by B alone

x × 2x  = 16
3x

∴   x =  24 days

Hence, option D is correct.

2
15 men take 20 days to complete a job working 8 hours a day. The number of hours a day should 20 men take to complete the job in 12 days
» Explain it
B
M1D1T1 = M2D2T2

⇒  15 × 20 × 8 = 20 × 12 × T2

⇒  T2 =  15 × 20 × 8  = 10 hours
20 × 12

Hence, option B is correct.

3
Raj and Ram working together do a piece of work in 10 days. Raj alone can do it in 12 days. Ram alone will do the work in
» Explain it
D
To solve this question, we can apply a short trick approach :

If A and B together can do a piece of work in x day and A alone can do it in y days, then B alonecan do the work in 
 
  xy  days.
y – x

Given,

Time taken by Raj and Ram together to finish a piece of work = x = 10 days

Time taken by Raj alone to finish the same piece of work = y = 12 days

By the short trick approach :

Ram alone can do the whole work in

  10 × 12  =  120  = 60 days
12 – 10 2

Hence, option D is correct.

4
A can do a piece of work in 20 days and B in 30 days. They work together for 7 days and then both leave the work. Then C alone finishes the remaining work in 10 days. In how many days will C finish the full work ?
» Explain it
C
Work done by A and B in 7 days

7  +  7  =  7
20 30 12

So,  remaining work

= 1 –  7  =  5
12 12

Now,   5  work done by C in 10 days.
12

∴  Time taken by C to finish the full work

= 10 ×  12  = 24 days
5

Hence, option C is correct.
5
A, B and C can do a job in 6 days, 12 days and 15 days respectively. After 1/8 of the work is completed, C leaves the job. Rest of the work is done by A and B together. Time taken to finish the work is
» Explain it
C
Remaining work

= 1 –  1  =  7
8 8

Work done by A and B in one day

1  +  1  =  1
6 12 4

∴  Time taken by A & and to finish 7/8 part of work

 =  7  × 4 =  7  = 3 1  days
8 2 2

Hence, option C is correct.