SBI PO Arithmetic Mains Questions Solved Problems with Detailed Solutions [Free PDF]
Last updated on Jun 12, 2025
Important SBI PO Arithmetic Mains Questions
SBI PO Arithmetic Mains Questions Question 1:
If one-fifth of a tank is filled by a pipe at the rate of 24 lit/min, one half of a tank is filled by another pipe at the rate of 30 lit/min and rest at the rate of 24 lit/min, the total time taken to fill the tank is 30 minutes. Time taken by pipe A to fill the tank is also 30 minutes. The total capacity of the tank is ________ liters and Time taken by pipe B to fill the tank is 15 minutes. The average rate at which the tank is filled if pipe B and pipe A together opened is ________.
Which of the following options satisfies the two blanks in the question?
A. 800 litre, 80 litre/min
B. 480 litre, 95 litre/min
C. 760 litre, 72 litre/min
D. 900 litre, 60 litre/min
Answer (Detailed Solution Below)
SBI PO Arithmetic Mains Questions Question 1 Detailed Solution
GIVEN :
If one-fifth of a tank is filled by a pipe at the rate of 24 lit/min.
One half of a tank is filled by another pipe at the rate of 30 lit/min.
Rest at the rate of 24 lit/min, the total time taken to fill the tank is 30 minutes.
Time taken by pipe A to fill the tank is also 30 minutes.
CALCULATION :
Let the total capacity of a tank be ‘n’ lit.
Average rate = total distance / time taken
⇒ Time taken by a pipe to fill 1/5th of a cistern = (n/5)/24 = n/120 min
⇒ Time taken by a pipe to fill 1/2nd of a cistern = (n/2)/30 = n/60 min
⇒ Rest part of a cistern remain to fill = n{1 – (1/5 + 1/2)} = n(1 – 7/10)
⇒ Rest part of a cistern remain to fill = 3n/10
⇒ Time taken by a pipe to fill rest of cistern = (3n/10)/24 = n/80 min
Total time taken by a pipe to fill cistern completely = (n/120 + n/60 + n/80) hr = 3n/80min
Given,
⇒ 3n/80 = 30
⇒ n = 800 litres
Pipe A’s 1 minute’s work = 1/30
Pipe B’s 1 Minute’s work = 1/15
Total time taken by pipe A and pipe B = 1/30 + 1/15 = 1/10
∴ Average rate = 800/10 = 80 litre/min.
SBI PO Arithmetic Mains Questions Question 2:
Directions: Information about three values have been given, you have to calculate the value of all three quantities and answer the question accordingly.
X: 60 Men could do a job in 40 days. Due to inclusion of some more Men, the work gets completed in 4/5 time. Fine the number of men added.
Y: A can finish the work in 5 days, while B takes 12 days to complete the same work. If A starts and they work on alternative days, Find the number of days taken to complete the work.
Z: A pipe can fill 40% of the tank in 6 hours. B can empty 30% of the same tank in 12 hours. If the tank is already half filled, find the time taken to fill the tank when both the pipes are opened together.Answer (Detailed Solution Below)
SBI PO Arithmetic Mains Questions Question 2 Detailed Solution
X: Number of men = 60
Time taken = 40
New number of men = a
New time = (4/5) × 40 = 32 days.
Now,
60 × 40 = 32 × a
a = 75
Number of new men = 75 - 60 = 15
Y: Let total work = LCM of 5,12 = 60 units
Work done by A in 1 day = 60/5 = 12 units
Work done by B in 1 day = 60/12 = 5 units
They will complete (5 + 12) units in 2 days.
17 × 3 = 51 units will be completed in 6 days.
Work remaining = 60 - 51 = 9 units
Time taken for 9 units by A = 9/12 = 0.75
Total time = 6.75 days.
Z: Time taken by A to fill 40% tank = 6 hours
Time taken to fill full tank = (6/40) × 100 = 15 hours.
Time taken by B to empty 30% tank = 12 hours.
Time taken to empty 100% tank = (12/30) × 100 = 40 hours
Let the capacity of tank = LCM of 15,40 = 120 units.
A will fill 8 units in an hour while B will empty 3 units in an hour.
Time taken to empty 60 units = 60/(8 - 3) = 12 hours.
X > Z > Y