## Time And Work MCQ’S

## Results

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### #1. If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work?

**Option A**

**1 ^{st} method:**

A and B complete a work in = 15 days

One day’s work of (A B) = 1/15

B complete the work in = 20 days;

One day’s work of B = 1/20

Then, A’s one day’s work

Thus, A can complete the work in = 60 days.

**2 ^{nd} method:**

(A B)’s one day’s % work = 100/15 = 6.66%

B’s one day’s % work = 100/20 = 5%

A’s one day’s % work = 6.66 – 5 = 1.66%

Thus, A need = 100/1.66 = 60 days to complete the work.

### #2. If A and B together can complete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in:

**Option B**

### #3. A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in

**Option B**

**1 ^{st} Method:**

(A B)’s one day’s work = 1/3 part

(A B) works 2 days together = 2/3 part

Remaining work = 1−2/3 =1/3 part

Hence, one day’s work of A = 1/6

Then, one day’s work of B =

So, B alone can complete the whole work in **6 days.**

**2 ^{nd} Method:**

(A B)’s one day’s % work = 100/3 = 33.3%

Work completed in 2 days = 66.6%

Remaining work = 33.4%

One day’s % work of A = 33.4/2 = 16.7%

One day’s work of B = 33.3 – 16.7 = 16.7%

B alone can complete the work in,

**6 days.**

### #4. A can complete a piece of work in 18 days, B in 20 days and C in 30 days, B and C together start the work and forced to leave after 2 days. The time taken by A alone to complete the remaining work is:

**Option C**

**1 ^{st} Method:**

**2 ^{nd} Method:**

% of work B completes in one day = 100/20 = 5%;

% of work C completes in one day = 100/30 = 3.33%;

% of work (A B) completes together in one day = 5 3.33 = 8.66%;

% work (A B) completes together in 2 days = 8.66 × 2 = 17.32%;

Remaining work = 100 – 17.32 = 82.68%;

% of work A completes in 1 day = 100/18 = 5.55%

Time taken to complete the remaining work by A = 82.68/5.55 = 15 days

### #5. Working 5 hours a day, A can Complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in:

**Option A**

**1 ^{st} Method:**

Working 5 hours a day, A can complete the work in 8 days i.e.

= 5 × 8 = 40 hours

Working 6 hours a day, B can complete the work in 10 days i.e.

= 6 × 10 = 60 hours

(A B)’s 1 hour’s work,

Hence, A and B can complete the work in 24 hours i.e. they require 3 days to complete the work.

**2 ^{nd} Method:**

% 1 hour’s work of A = 100/40 = 2.5%

% 1 hour’s work of B = 100/60 = 1.66

(A B) one hour’s % work,

Time to complete the work,

Then,

They need 3 days, working 8 hours a day to complete the work.

### #6. Ganga and Saraswati, working separately can mow field in 8 and 12 hours respectively. If they work in stretches of one hour alternately. Ganga is beginning at 9 a.m., when will the moving be completed?

**Option C**

**1 ^{st} Method:**

Whenever, workers are working alternatively on one work, we take 2 as 1 unit

In this case, we take 2 hours as 1 unit.

Part of the field moved by Ganga and Saraswati in 2 hours (1 unit) = 1/8 1/12 = 5/24

Time taken to complete the work,= 1/5/24 =24/5 unit of time

Then actual time taken by them to complete the work,

The work starts at 9 a.m. then it will complete at 6:36 pm

**2 ^{nd} Method:**

% of the field moved by Ganga and Saraswati in 2 hours (1 unit),

= 12.5 8.33

= 20.83%; Time taken to move the whole field,

= 100%/20.83%

= 4.8 unit of time;

Hence, actual time = 2 × 4.8 = 9.6 hours.

The work starts at 9 a.m. then it will complete at 6:36 pm

### #7. If 10 men can do a piece of work in 12 days, the time taken by 12 men to do the same piece of work will be:

**Option B**

Here, we use work equivalence method;

10*12 = 12*x;

Or, x = 10 days;

**To understand the work equivalence method, we use a graphic as follows:**

Men Days

10 ↓ 12

12 ↑ x (let)

Here, the two arrows, downward (↓) and upward (↑) show variation between men and days.

**[If downward arrows show decrements then upward arrows show increments and vice-verse.]**

Thus,

### #8. To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

**Option A**

B alone can complete the work in

### #9. If 10 men or 20 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 4 boys in 20 days?

**Option A**

10 men = 20 boys

→1 men = 2 boys

8 men = 2 × 8 boys = 16 boys

Then,

(16 boys 4 boys) = 20 boys can make 260 mats in 20 days

Now,

**It can be calculated by work equivalence method:
**20 × 260 × 20 = x × 20 × 20

x = 260 mats

### #10. A complete 7/10 of a work in 15 days, then he completed the remaining work with the help of B in 4 days. In how many day A and B can complete entire work together?

**Option C**

Rest work = 1 – 7/10 = 3/10 part

Given, That

(A B) completed the 3/10 of work in 4 days

So, (A B)’s 1 day’s work =

Hence,

(A B) can complete the work in