Quantitative Aptitude Problems with Solutions

1. TIME AND WORK

2. Work from Days
If A can do a piece of work in n days,
then A's 1 day's work = 1 .
n
• Days from Work:
• If A's 1 day's work = 1 , then A can finish the
n
work in n days.

3. Ratio
• If A is thrice as good a workman as B, then:
Ratio of work done by A and B = 3 : 1.
Ratio of times taken by A and B to finish a
work = 1 : 3.

4. Question
• Worker A takes 8 hours to do a job.
Worker B takes 10 hours to do the same
job. How long should it take both A and B,
working together but independently, to do
the same job?
• A. 4 2/9 days
• B. 4 4/9 days
• C. 4 5/9 days
• D. 4 7/9 days

5. • Answer: Option B
• Explanation:
• A’s 1 hour’s work = 1/8
• B’s 1 hour’s work = 1/10
• (A+B)’s 1 hour’s work = (1/8+1/10) = 9/40
• Both A and B will finish the work in 40/9= 4 4/9
days

6. Question
• Rohan can do a piece of work in 36 days
but with the help of Mohan he can
complete the work in 24 days. Find the no
of days in which Mohan alone can
complete the work?
• A 80 days
• B 84 days
• C 72 days
• D 74 days

7. C 72 days
• Total work done by Rohan and
Mohan=L.C.M of 36 & 24= 72 days
• Work rate of Rohan= 72/36=2
• Combine work rate(R+M)=72/24=3
• Work rate of Mohan=3-2=1
• No.of days required by Mohan=72/1
=72 days

8. Question
• A and B together can complete a piece of
work in 4 days. If A alone can complete
the same work in 12 days, in how many
days can B alone complete that work?
• A. 6 days
• B. 4 days
• C. 8 days
• D. 9 days

9. • Answer: Option A
• Explanation:
• (A+B)’s 1 day’s work = ¼
• A’s 1 day’s work = 1/12
• B’s 1 day’s work = ¼ - 1/12 = 1/6
• B alone can complete the work in 6 days.

10. Question
• A and B can do a work in 25 days and 20
days. Both together work for 5 days and
then A leaves off. How many days B take
to finish the remaining work?
• A 16 days
• B 11 days
• C 12 days
• D 14 days

11. B 11 days
• A can finish work in 25 days & B can finish
the work in 20 days
• Total work done=100(L.C.M of 25&20)
• A’s Contribution=100/25=4
• B’s Contribution =100/20=5
• First we need to calculate 5 days
work=9x5=45
• Remaining work=100-45=55
• B require No.of days=55/5=11 days

12. Question
• A is twice as good a workman as B and
together they finish a piece of work in 18
days. In how many days will A alone finish
the work?
• A. 27 days
• B. 24 days
• C. 28 days
• D. 29 days

13. • Answer: Option A
• Explanation:
• (A’s 1 day’s work) : (B’s 1 day’s work) = 2 : 1
• (A+B)’s 1 day’s work = 1/18
• Divide 1/18 in the ratio 2 : 1
• A’s 1 days work = 1/18 x 2/3 = 1/27
• So, A alone can finish the work in 27 days.

14. Question
• A can finish a work in 24 days. B in 9 days
and C in 12 days. B and C start the work
but are forced to leave after 3 days. The
remaining work was done by A in
• A 9 days
• B 10 days
• C 11 days
• D 12 days

15. B 10 days
• Total work done= L.C.M of 24,9,8=72
• Work rate of A =72/24=8
• Work rate of B= 72/9=8
• Work rate of C=72/12=6
• In 3 days B & C can complete
work=14x3=42 part
• Remaining work= 72-42=30(A’s Work)
• No of days required by A= 30/3= 10 days

16. Question
• A and B working separately can do a piece
of work in 9 and 12 days respectively. If
they work for a day alternately, A
beginning, in how many days, the work will
be completed?
• A. 10 ¼ days
• B. 10 ½ days
• C. 8 ¼ days
• D. 8 ½ days

17. • Answer: Option A
• Explanation:
• (A+B)’s 2 day’s work = 1/9+1/12 = 7/36
• Work done in 5 pairs of days = 5x7/36=35/36
• Remaining work = 1 – 35/36 = 1/36
• On 11th day, it is A’s turn.
• 1/9 work done by him in 1 day.
• 1/36 work done by him in (9x1/36) = ¼ days.
• Total time taken = 10 + ¼ = 10 ¼ days.

18. Question
• A and B can do a piece of work in 20 days
and 12 days resp. A alone started the
work and then after 4 days B joined him till
the completion of work. How long did the
work last?
• A 10 days
• B 12 days
• C 13 days
• D 11 days

19. A 10 days
• Total Work Done by A & B =L.C.M OF
20&12 =60
• Work done by A=60/20=3 part
• Work done by B =60/12=5 part
• In 4 days work done= 4x3=12
• Remaining work=60-12=48
• Combine work rate=A+B=3+5=8
• No.of days both A&B work=48/8=6
• Total no.of days work last=6+4=10 days

20. Question
• 45 men can complete a work in 16 days.
Six days after they started working, 30
more men joined them. How many days
will they now take to complete the
remaining work?
• A. 6 days
• B. 4 days
• C. 8 days
• D. 9 days

21. • Answer: Option A
• Explanation:
• 45 men can complete the work in 16 days.
• (45x16) men can complete the work in 1 day.
• 1 man’s 1 day’s work = 1/720
• 45 men’s 6 day’s work = 45/720 x 6 = 3/8
• Remaining work = 1 – 3/8 = 5/8
• 75 men’s 1 day’s work = 75/720 = 5/48.
• Now, 5/48 work is done by them in 1 day.
• So, 5/8 work is done by them in 48/5 x 5/8 = 6 days

22. QUESTION
• IF 5 MEN OR 19 WOMEN CAN DO A
PIECE OF WORK IN 19 DAYS. IN HOW
MANY DAYS CAN 3 MEN AND 6
WOMEN WILL DO THE SAME WORK?
• A 10
• B 15
• C 18
• D 20

23. B-15 DAYS
• 5M/9W Can do work in 19 days.3M & 6W
=d2(find)
• 5MX 19=(3M+6W)d2
• 1W=5/9M, 6W=5/9X6=10/3M
• 5MX19=(3M+6W)d2
• 5MX19=(3M+10/3M)d2
• 5X19=(3+10/3)d2
• d2= 15 days

24. Question
• Sachin can do a piece of work in 10 days
while Rahul can do it in 15 days. They
work together for 5 days and the rest work
is done by Virat in 2 days. If they get Rs
4500 for the whole work what is the share
of Virat?
• A 700 Rs
• B 780 Rs
• C 800 Rs
• D 750 Rs

25. D 750 Rs
• Sachin Work= 10 , Rahul Work=15
• Total work done by both= 30
• Work rate of Sachin= 30/10=3
• Work rate of Rahul=30/15=2
• One day Sachin & Rahul can complete
3+2=5 piece of work
• In 5 days work complete=5(sachin & rahul
work)x 5(no.of days)=25
• S & R: V=25:5=5:1
• Virat Share=4500/6x 1=750 Rs

26. THANK YOU