Time and Work Question, Formula Tricks

Hey Guys, Welcome back to Learn Aptitude. Today I will discuss the full concept of Time Work, shortcut tricks, Formula  and I will all variant of Time and Work Questions.

In India 80% people are facing problems in Time and Work Questions. It is not so difficult, but it is a conceptual trick. Just clear your concept about Time and work and your rest work is done.

Basic Concept of Time and Work

Let us Assume there are two people, first one is Ram and Second one is Hari. In one day Ram can make 3 dolls and Hari can make 5 dolls. Now observe the following Time and Work table.

Time Ram Hari
1- Day
3 Dolls
5 Dolls
7-Days

7 × 3 =21 Dolls

7 × 5 =35 Dolls

30-Days

30 × 3 = 90 Dolls

30 × 5 = 150 Dolls 

From the above table, we can observe that Ram is taking more time than Hari for making Dolls.While Hari is producing more dolls in less time. So we can conclude that Time and work are indirectly propotional to each other.

Time and Work Formulas

  • Work Done in 1-Days= 1/Number of Days
  • Work Done in n days = Work Done in 1 Days × n days
  • Number of Days= Work Done Days/ work done in 1 days

Time and Work Questions with Answers

Q.1 A can complete a work within 6 days while B can complete that work within 5 days. If both A and B work together, then how many days, then will take to complete the same work?

(A) 10 Days
(B) 11 Days
(C) 12 Days
(D) 13 Days

Answer: (B) 11 Days

Solution: A =6 Days

B= 5 Days

L.C.M of A and B = 30

Days will be taken A and B = LCM/ A's Days + LCM/B's Days= (30/6) + (30/5)= 5 + 6= 11

∴ If A and B will work together then they will take 11 days to complete the work.

Q.2  Two People both P and Q can complete a work in 15 days and Q alone can complete the work in 20 days, then how many days P will take to complete the work?

(A) 30 Days
(B) 23 Days
(C) 60 Days
(D) 83 Days

Answer: (C) 60 Days

Solution: P+Q= 15 days

Q= 20 days

LCM of P and Q = 60

P and Q can do in 1 day= LCM/15= 4

Q can do in 1 day= LCM/20= 60/20=3

Hence P can do in 1 Day= 4-3=1

Finally, P can alone complete the work = 1 × 60= 60days

Q.3  Ram can complete a wall in 7 days of working 9 hours each while Laxman can complete in 6 days of working 7 hours each. How many days it will take if they work together 42/5?

(A) 3 Days
(B) 6 Days
(C) 9 Days
(D) 8 Days

Answer: (A) 3 Days

Solution: Ram can complete the work in 7 × 9 = 63 hours

Laxman can complete the work in 6 × 7 = 42 days

Ram's 1 hour work= 1/63

Laxman's 1 hour Work= 1/42

Both Ram and Laxman's 1 hour work will be (1/63) + (1/42)= 5/126

Hence, both will complete the work = (126/5)hrs

Days it will take to complete if they work together for 42/5 hours= (126/5) × ( 5/42) = 3 days

Q.4 Y can work twice of X. If both X and Y complete the work together within 30 days then how many days Y will take to complete the work alone?

(A) 45 Days
(B) 10 Days
(C) 58 Days
(D) 60 Days

Answer: (A) 45 Days

Solution:

 

Time and Work solutions

Q.5 Between two people A and B, B can complete a work in 20 days while A is 30% more efficient than B. How many days A will take to complete the work?

(A) 22 Days
(B) 24 Days
(C) 36 Days
(D) 38 Days

Answer: (B) 24 Days

Solution: As Per question A can work 30% more than B and we can write the ratio of their work as 120:100= 6:5

Lets assume A can complete the work within x days

Finally, we can re-write it as 6:5 :: x:20

⇒5x = 120

⇒x = 120/5= 24days

Q.6 A woman can complete a certain job in 24 days and a man can complete the same work in half the time taken by the Woman. If they work together, then how many days they will complete the work?

(A) 22 Days
(B) 15 Days
(C) 8 Days
(D) 6 Days

Answer: (C) 8 days

Solution: As per Question Woman can complete the work i 24 days 

1 day's work of man = 1/24 and

A Man can complete the work  in 24/2= 12 days.

1 day's work of woman= 1/12

Man's 1 hour Work + Woman's 1 hour Work = (1/24) + (1/12) = 3/24= 1/8

Both Man and woman will complete the work in 8/1= 8 days.

Q.7 I can paint a wall within 24 hours and with the help of my brother, I can paint it by 8 hours. If my brother will paint alone, then how many hour he will take?

(A) more than 4 days
(B) less than 4 days but greater than 3 days
(C) less than 4 days
(D) more than 4 days but less than 5 days

Answer: (D) more than 4 days but less than 5 days

Solution: I can complete the paint alone in 24 hours

1 hour's work = 1/24

With brother, I take 6 hours

1 hour's paint with my brother = 1/6

1 hour's alone paint of my brother  (1/6) - (1/24) = 5/24

Alone my brother will take time = 24/5= 4.8days

Q.8 A water tank has two holes. The first hole alone can make the water tank empty in 9 minutes where the second hole alone can make the tank empty in 6 minutes. If water flow remains at the constant rate and both the hole started to make the tank empty, then how many minutes it will take to make the tank empty.

(A) more than 4 days
(B) less than 4 days but greater than 3 days
(C) less than 4 days
(D) more than 4 days but less than 5 days

Answer: (B) less than 4 days but greater than 3 days

Solution: First tank makes the tank empty in 9 minutes

In 1 minutes it will make 1/9

Second tank makes the tank empty the in 6 minutes

In 1 minutes it will make 1/6

So, if both the holes will work at same time then in 1 minute (1/9) + (1/6) = 5/18

∴ Required time = 18/5 = 3.6

Q.9 Papu can make half sweet than Lipu in three-fourth of  the time. If they work together then they take 30 days to complete the sweet production then how many days Lipu alone will take to complete the work?

(A) 30
(B) 40
(C) 50
(D) 45

Answer: (A) 30

Solution: Let Lipu take x days to complete sweet production.

1 days work = 1/x

Lipu and Papu will complete sweet production in 30 days

In 1 days work= 1/18

Papu takes {2 × (3x/4)= 3x/2 days to complete it

As per Question we have (1/x) + (3x/2) = 1/18

By solving abopve, we have x= 30

Q.9 Papu can make half sweet than Lipu in three-fourth of  the time. If they work together then they take 30 days to complete the sweet production then how many days Lipu alone will take to complete the work?

(A) 30
(B) 40
(C) 50
(D) 45

Answer: (A) 30

Solution: Let Lipu take x days to complete sweet production.

1 days work = 1/x

Lipu and Papu will complete sweet production in 30 days

In 1 days work= 1/18

Papu takes {2 × (3x/4)= 3x/2 days to complete it

As per Question we have (1/x) + (3x/2) = 1/18

By solving abopve, we have x= 30

Q.10 Two people A and B can do a certain work in 60 days and 40 days respectively. If they both work for 6 hours, then how much fraction of the work will be completed in 6 days?

(A) 1/9
(B) 1/8
(C) 1/24
(D) 1/6

Answer: (B) 1/8

Solution: A can do the work in 60 days

In 1 day it will do 1/60 fraction

B can do the work in 40 days

In 1 days B can do 1/40 fraction

In 1 day both A and B can complete (1/60) + (1/40) = 1/24 fraction

In 4 days = (1/24) × 4= 1/8