Mains Level Quantitative Aptitude Questions for IBPS PO, SBI Clerk Mains, IBPS RRB PO, IBPS RRB Clerk and RBI Assistant Mains Exams with Detailed Solution

Directions: Read the following questions carefully and choose the right answer. 
1
Two pipes A and B can fill 20 gallons and 30 gallons of water in one hour respectively and the third pipe C can empty ‘x’ gallons of water in an hour. If all the three are opened together, the tank gets filled in 15 hours, and when pipe A and B are opened together the tank gets filled in 12 hours, then find how much gallons of water are drained by pipe C in an hour?
» Explain it
E
Gallons of water filled by pipe A and B in one hour = 20 + 30 = 50

Capacity of the tank = 50 × 12 = 600 gallon

Now three pipes together,

⇒ (20 + 30 – x) × 15 = 600

⇒ 300 + 450 – 15x = 600

⇒ 15x = 750 – 600

⇒ X =  150  = 10 gallons.
15

Hence, option E is correct.
2
Three workers Trump, Putin and Jinping are appointed to do a job. They together started the job but Jinping left after 3 days when 37% of the job was done. The remaining job was completed by Trump and Putin in 7 days. The ratio of efficiency of Trump and Putin is 4 : 5. Find the number of days required by the slowest worker to complete the entire job alone?
» Explain it
E
Let x, y and z are the one day’s work of Trump, Putin and Jinping respectively.

According to the question,

⇒ 3 × (x + y + z) = 37% of the work

⇒ 7 × (x + y) = 63%

⇒ x + y = 9%

∵ The ratio of efficiency of Trump and Putin is 4 : 5,

∴ 5x = 4y and x = 4%, y = 5% work per day.

It implies Trump can complete the job and in 25 days and Putin in 20 days.

In 3 days (x + y + z) do 37% of the work

Out of this Trump and Putin would do 27% work = (3 × 9%) of the work.

Remaining work = 37% – 27% = 10% (done by Jinping in 3 days)

∴ The work of z =  10  = 3.33% work per day
3

∴ Jinping is the slowest and he would do the work in 30 days.

Hence, option E is correct.
3
JK and his business partner JP started a joint venture company with initial investment in the ratio of 7 : 2. The company earned equal income for the first and second year and the profit is divided equally between them every year. To equalise the initial investment JP had to pay his entire share of income for the 1st year and half his share of income in the 2nd year. Find the ratio of initial investment to total income.
 
» Explain it
E
Let the initial investment of JK be ‘7m’

∴ The initial investment of JP will be ‘2m’

Also, let the total income generated in two years be 4n

Though the profit for the two years is divided equally between them,

∴ JK’s share in income will be = 2n

And JP’s share in income will be = 2n

Now to equalise initial investment,

⇒ 2m +  3n  = 7 m
2

⇒  3n  = 5 m
2

⇒  m  =  3
n 10

∴ Ratio of initial investment and total income

9m  =  27
4n 40

Hence, option E is correct.
4
The ratio of speeds of a tiger and horse is 3 : 2. Both start from place A at the same time and reach place B, which is 75 km away from place A at the same time as the tiger lost about 12.5 minutes while hunting a deer. Find the speed of the horse.
» Explain it
A
Let speed of the horse be x km/h.

∴ Speed of the tiger =  3x  km/h
2

Now, according to the question,

⇒  75  –  75  =  125
x 3x/2 10 × 60

⇒  75  –  50  =  5
x x 24

⇒ x =  25 × 24  = 120 
5

Hence, option A is correct.
5
The ratio between the present ages of Amon and Chan is 3 : 4. The ratio of Bevan’s age after 5 years to Chan’s age 1 year ago is 4 : 3 and four times the difference in ages of Chan and Amon is one more than the age of Bevan. Find the average of the present ages of Amon and Chan.
» Explain it
C
Let Amon’s age = A, Bevan’s age = B, and Chan’s age = C

Then, according to the question,

⇒  A  =  3  ................(i)
C 4

⇒  B + 5  =  4  ................(iI)
C – 1 3

⇒ 4 × (C – A) = B + 1 ------------------(iii)

After solving these equations,

⇒ A = 12 

⇒ C = 16

Average of ages of Amon and Chan =  12 + 16  = 14
2

Hence, option C is correct.