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*Time and work questions solutions *

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**Difficulty Level - Medium**

**Difficulty Level - Medium**

1. A
can work on 1km railway track in 1 day. In how many days, will he able to

*the work on 12km railway track?***complete**
Soln: no. of days = total
work / work done in 1 day

Therefore,
no. of days taken = 12/1 = 12 days

2. A
can complete the work in 15 days. What fraction of work will be completed in 1
day?

Soln.: Let the total work is 1 unit.

Work in 1day = total
work/no. of days to complete

= 1/15

^{th}of work
3. A
can do a piece of work in 3 days and B can do a piece of work in 5 days. In how
many days will the work be completed if both A and B work together?

Soln.:

**Using formula:****Work done by A in 1 day = 1/3**

Work done by B in 1 day = 1/5

Total work done by A and B in
1 day = 1/3 + 1/5 = 8/15

Therefore, no. of days to
complete work by A and B together = 1/(Total work) = 1/(8/15) = 15/8 days which
is less than 3 and 5

**Using shortcut/analysis/assumption**

**Let us consider the total work be 15 units (LCM of 3 and 5)**

So work done by A in 1 day =
15/3 = 5 units

Similarly work done by B in 1
day = 15/5 = 3 units

So total work done by A and B
in 1 day = 5 + 3 = 8 units

Therefore, no. of days to
complete total work i.e. 15 units = total work/work done in 1 day = 15/8 days

**Note:**

**a. Work done by A and B in 1 day**

**will always be greater than**that of A and B individually

b. No. of days taken by A and B together

**will always be less than**that of A and B individually
4. A
can do a piece of work in 6 days, B can do a piece of work in 4 days and C can
do a piece of work in 12 days. Find the no. of days to complete the work if A,
B and C work together?

Soln.:

**Using formula:****Work done by A in 1 day = 1/6**

Work done by B in 1 day = ¼

Work done by C in 1 day = 1/12

Total work done by A, B and C
in 1 day = 1/6 + ¼ + 1/12 = 12/24 = 1/2

Therefore, no. of days to
complete work by A, B and C together = 1/(Total work) = 1/(1/2) = 2 days which
is less than 4, 6, 12

**Using shortcut/analysis/assumption**

**Let us consider the total work be 24 units (LCM of 4, 6, 12)**

So work done by A in 1 day =
24/4 = 6 units

work done by B in 1 day = 24/6
= 4 units

work done by C in 1 day =
24/12 = 2 units

So total work done by A, B and
C in 1 day = 6 + 4 + 2 = 12 units

Therefore, no. of days to
complete total work i.e. 24 units = total work/work done in 1 day = 24/12 = 2
days

The above Note is
valid here as well.

5. A
can do a piece of work in 6 days and B can do a piece of work in 12. Find the
no. of days to complete the work if A and B work alternatively?

Soln.:

**Using formula:****Work done by A in 1 day = 1/6**

Work done by B in 1 day = 1/12

Total work done by A and B
working 1 day each = 1/6 + 1/12 = 3/12 = ¼

Therefore, 1/4

^{th}of work is done in 2days.
No. of days to complete total
work if A and B work alternatively = 1/((1/4)/2) = 8 days

**Using shortcut/analysis/assumption**

**Let us consider the total work as 12 units (LCM of 6, 12)**

So work done by A in 1 day =
12/6 = 2 units

work done by B in 1 day =
12/12 = 1 unit

Total work done by A and B
working 1 day each = 2 + 1 = 3 units in 2 days

Therefore, work done in 1 day
= work/no. of days = 3/2 units

No.
of days to complete work = total work/work in 1 day = 12/(3/2) = 8 days

6. 30
men can complete a job in 40 days. Then 25 men can complete the same job in how
many days?

Soln.: As per M1D1 =
M2D2

30
* 40 = 25 * x => x
= 30 * 40/25 = 48 days

7. 30
men can complete 1500 units in 24 days working 6hrs a day. In how many days can
18 men can complete 1800 units working 8 hrs a day?

Soln.: As per the formula (from my earlier blog), M1D1h1/W1 = M2D2h2/W2

=> 30*24*6/1500 = 18*x*8/1800

=> x = 36 days

8. A and B can do a work in 10 and 15
days respectively. Then combinedly A & B, in how many days the work will be
completed?

Soln.: As per the formula (from my earlier blog), x*y/(x + y)

A and B together can complete the work in 10 * 15/(10 + 15) = 6 days

A and B together can complete the work in 10 * 15/(10 + 15) = 6 days

9. A can do a work in 10 and, A and B
together can do a work in 6 days. In how many days B can complete the same
work?

Soln.: As per the formula (from my earlier blog), x*y/(x - y)

B alone can complete the work in 10 * 6/(10 - 6) = 15 days

B alone can complete the work in 10 * 6/(10 - 6) = 15 days

10. A is twice faster than B and B can
complete in 12 days alone. Find the number of days to complete if A and B
together work?

Soln.: Given B works in 12 days

A is twice faster
than B => A takes 2 times less time than B

Therefore, A
completes work in 12/2 = 6 days

A
and B together can complete in 12 * 6/(12 + 6) = 4 days