Numerical Ability Test

Result

Numerical Ability Test - 24

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Weekly Quiz Competition

Question 1
5 / -1

If 10 men or 16 boys can build a house in 60 days, in how many days can 25 men and 16 boys build this house?

A
17 days

B

C

D
None of these

Solution

Portion of house built by 10 men or 16 boys in one day = 1/60

Portion of house built by 1 man in 1 day = 1/(10 × 60) = 1/600

Portion of house built by 1 boy in 1 day = 1/(16 × 60) = 1/960

Portion of house built by 25 men and 16 boys in 1 day = (25/600) + (16/960) = 7/120

Number of days taken by 25 men and 16 boys to build the house = 1/(7/120) = 120/7 = 17 ¹/₇ days
Question 2
5 / -1

Two pipes, when working one at a time, can fill a cistern in 3 hours and 4 hours, respectively while a third pipe can drain the cistern empty in 8 hours. All the three pipes were opened together when the cistern was 1/12 full. How long did it take for the cistern to be completely full?

A
2 hours

B
1 hour 45 minutes

C
2 hour 11 minutes

D
2 hour 10 minutes

Solution

Given:

First pipe can fill the cistern = 3 hours

Second pipe can fill the cistern = 4 hours

Third pipe can drain the cistern = 8 hours

Calculation:

Let the total amount of work in filling a cistern be 24 units. (LCM of 3, 4 and 8)

Work done by pipe 1 in 1 hour = 24/3 = 8 units.

Work done by pipe 2 in 1 hour = 24/4 = 6 units.

Work done by pipe 3 in 1 hour = 24/ (-8) = -3 units

Total work done in 1 hour = 8 + 6 – 3 = 11 units

The time required to complete 11/12^th of the work = 11/12 × 24/ 11 = 2 hours

∴ The correct answer is 2 hours.
Question 3
5 / -1

A and B together are supposed to do 13/15 of the work and B and C together 11/20 of the work. If the difference between wages of A and C is Rs. 7600, then the total wages of A and C is:

A
Rs. 14000

B
Rs. 36000

C
Rs. 18000

D
Rs. 56000

Solution

Given:

Difference between wages of A and C = Rs. 7600

Formula Used:

Share in wages = Work done/Total work × Total wages

Calculation:

Let total work be 60 unit,

Work done by A and B = 13/15 × 60 = 52 unit

⇒ Work done by C = 60 – 52 = 8 unit

Work done by B and C = 11/20 × 60 = 33 unit

⇒ Work done by A = 60 – 33 = 27 unit

Work done by B = 60 – 27 – 8 = 25 unit

According to the question,

27 – 8 = 19 unit = 7600

⇒ 1 unit = 400

Total wages of A and C = (27 + 8) = 35 units = 35 × 400 = Rs. 14000
Question 4
5 / -1

A,B and C can do a piece of work in 30 days, 40 days and 50 days, respectively. Beginning with A, if A, B and C do the work alternatively then in how many days will the work be finished?

A

B

C
36

D

Solution

Given:

A can do a piece of work = 30 days

B can do a piece of work = 40 days

C can do a piece of work = 50 days

Formula used:

Total work = efficiency × time

Calculation:

According to the question:

⇒ (20 + 15 + 12) = 47 units = 3 days

⇒ 47 × 12 = 564 units = 3 × 12 = 36 days

⇒ (564 + 20 + 15) = 599 units = 38 days
Question 5
5 / -1

A and B can complete a task in 12 days. However, A had to leave a few days before the task was completed and hence it took 16 days in all to complete the task. If A alone could complete the work in 21 days, how many days before the work getting over did A leave?

A
7

B
5

C
9

D
3

Solution

Given A alone can complete the work in 21 days

A and B together can complete the same work in 12 days

⇒ Total work = L.C.M of (12, 21) = 84

⇒ One day work of A = 4

⇒ One day work of (A + B) = 7

⇒ One day work of B = 3

Let A worked for x days and B worked for 16 days

⇒ 4x + 3 × 16 = 84

⇒ x = 9 days

∴ A left the work before (16 - 9 =) 7 days.
Question 6
5 / -1

A man and a woman can finish a work together in half the time taken by a woman and a boy together. A boy can finish the work alone in 20 days and 2 women together can finish it in 30 days. In how many days will the work be finished by 4 men?

A
2

B
2.14

C
2.5

D
3

Solution

Given:

Time taken by (man + woman) = (1/2) × Time taken by (woman + boy)

A boy alone can finish the work = 20 days

2 women can finish the work = 30 days.

Concept used:

If total work is constant then,

Time ∝ (1/efficiency)

Formula used:

Total work = efficiency × time

Calculation:

2 women can finish the work = 30 days.

1 woman can finish the work = 30 × 2 = 60 days

Now,

Time taken by (man + woman) = (1/2) × Time taken by (woman + boy)

Time taken by (man + woman) : Time taken by (woman + boy) = 1 : 2

Efficiency of (man + woman) : Efficiency of (woman + boy) = 2 : 1

(Woman + boy) = (3 + 1) = 4

⇒ 1 unit = 4 units/day

⇒ 2 units = 4 × 2 = 8 units/day

Efficiency of (man + woman) = 8

Efficiency of man = 8 - 1 = 7 units/day

Time taken to complete the work by 4 men = 60/(4 × 7)

⇒ 60/28 = 15/7 = 2.14 days

∴ The correct answer is 2.14 days.
Question 7
5 / -1

A group of men decided to do a job in 11 days but 16 men left the work after each day. The work, as a result, got completed in 15 days. How many men were there initially in the group?

A
400

B
480

C
420

D
450

Solution

Given:

A group of men decided to do a job in 11 day, but 16 men dropped out every day.

The job was completed in 15 days.

Concept used:

Total work = Efficiency of each worker × Number of days to finish × Number of total workers

Calculation:

Let there be Q men initially with the efficiency of 1 unit per day.

Total work = Q × 1 × 11 = 11Q units

According to the question,

Q + (Q - 16) + (Q - 16 × 2) + .... + (Q - 16 × 14) = 11Q

⇒ 15Q - (16 + 32 + .... + 224) = 11Q

⇒ 4Q = 16 × 105

⇒ Q = 420

∴ There were 420 men initially.
Question 8
5 / -1

An inlet pipe can fill an empty tank in hours while an outlet pipe drains a completely filled tank in hours. The tank is initially empty. and the two pipes are alternately opened for an hour each, till the tank is completely filled, starting with the inlet pipe. In how many hours will the tank be completely filled?

A
24

B

C

D

Solution

Given:

An inlet pipe can fill an empty tank in hours while an outlet pipe drains a completely filled tank in hours.

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day

Calculation:Time taken by A = 9/2 hours

Time taken by B = 36/5

Capacity of tank = LCM(9/2, 36/5) = 36 units

Efficiency of A = 36/(9/2) = 8 units

Efficiency of B = 36/(36/5) = - 5 units

tank filled in 2 hours = 8 - 5 = 3 units

tank filled in 20 hours = 30 units and Please note that after 20 hours, the remaining capacity = 6 units Now in the 21st hour, pipe A will work and fill the tank so no need to add time after that.

Time taken by pipe A to fill 6 units = 6/8 = 3/4 hours

So,

Shortcut Trick
Question 9
5 / -1

A and B can complete a piece of work together in 20 days. They start work together but A had to leave 5 days before the work finally got over. If B finishes the remaining in 18 days, then how long will B take to complete the work separately.

A
72 days

B
64 days

C
100 days

D
120 days

Solution

Formula used:

Total work = Efficiency × Time

Calculation:

∵ A left before 5 days due to which B had to work for 18 days

Let the efficiency of A and B be x and y respectively

5-day work of A and B together = 18 days work of B

⇒ 5 (x + y) = 18y

⇒ x : y = 13 : 5

Total work = (13 + 5) × 20 = 360 units

∴ Time is taken by B alone to complete the work = 360/5 = 72 days
Question 10
5 / -1

Numan does half the work as Gagan in 4/5 of the time. If together they take 16 days to complete a piece of work, then how long will it take Gagan to complete the work?

A
23 day

B
24 days

C
25 day

D
26 days

Solution

Given:

Numan does half the work as Gagan in 4/5 of the time.

Together they take 16 days to complete a piece of work

Calculation:

According to the question,

Numan × 4/5 = Gagan × 1/2

⇒ Numan = Gagan × 5/8

⇒ Numan/Gagan = 5/8

So, Numan’s efficiency = 5 unit/day. & Gagan’s efficiency = 8 unit/day.

Now,

Total work = 16 × (5 + 8)

⇒ 16 × 13

Time taken by Gagan = (16 × 13)/8

⇒ 26 Days

∴ Gagan will take 26 days to complete the work.