Quantitative Aptitude Quiz for UPSI : 01 May 2021

1. Rahul and Ravi undertook to do a piece of work for Rs. 9000. Rahul alone could do the work in the 16 days and Ravi in 24 Days. With the assistance of Kamlesh, they finished the work in 8 days. How much money should be given to Kamlesh?

a) Rs.

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2400
b) Rs. 1800
c) Rs. 1200
d) Rs. 1500


2. Raja and Kundan together can build a wall in 20 days, Kundan and Mahesh can build the same wall in 30 days and Mahesh and Raja can build the same wall in 24 days. In how many days can all three of them complete the same wall while working together?

a) 12
b) 16
c) 18
d) 24

3. What is the remainder when (256)^47 is divided by 15?

a) 2
b) 1
c) 3
d) 4


4. A train starts from a place A at 8 : 00 a.m. and arrives at another place B at 1 : 30 p.m. on the same day. If the speed of the train is 30 km/hr, then what will be the distance (in km) covered by the train?

a) 155 km
b) 185 km
c) 175 km
d) 165 km

5. The simple interest on a sum is 5/9 of the principal for 25 years. What is the rate (in percentage) of interest per annum?

a) 10/3%
b) 20/3%
c) 10/9%
d) 20/9%

6. Evaluate (3 × 25 ) ÷ 5 - 20 × 4 + 75

a) 5
b) 10
c) 15
d) 20

7. Rahul’s salary is 40% more than Mohit’s salary. If Rahul’s salary is increased by 60% and Mohit’s salary is decreased by 20%, then Rahul’s salary will be how much percentage of Mohit’s salary?

a) 300%
b) 240%
c) 250%
d) 280%

8. If the profit on selling an article for Rs. 425 is the same as the loss on selling it for Rs. 355, then the cost price of the article is

a) 520
b) 390
c) 340
d) 350

9. The cost price of 25 books is equal to the selling price of 20 books. The profit percent is

a)  30%
b)  15%
c)  20%
d)  25%

10. Average weight of P and Q is 32 kg. Average weight of Q and R is 43 kg. Average weight of P and R is 51 kg. What is the average weight (in kg) of P, Q and R?

a) 42 kg
b) 44 kg
c) 36 kg
d) 40 kg
 
Solution:
1.
⇒ Work done by Rahul in 8 days = 8 × (1/16) = 1/2
⇒ Work done by Ravi in 8 days = 8 × (1/24) = 1/3
It means, Rahul and Ravi, done 1/2 and 1/3rd of work, respectively, in 8 days
⇒ Work done by kamlesh = {1 – (1/2 + 1/3)} = 1 – 5/6 = 1/6
⇒ Rahul’s share: Ravi’s share : Kamlesh's share = 1/2 : 1/3 = 3 : 2
⇒ Kamlesh’s share = (1/6) × 9,000 = 1500
∴ Kamlesh’s share is Rs. 1500
2.
Work done by Raja and kundan in one day = (1/R) + (1/K) = 1/20
Work done by Mahesh and kundan in one day = (1/M) + (1/K) = 1/30
Work done by Raja and Mahesh in one day = (1/R) + (1/M) = 1/24
Adding the above three equations we get,
⇒ 2{(1/R) + (1/K) + (1/M)} = [(1/20) + (1/30) + (1/24)] = 15/120 = 1/8
⇒ (1/R) + (1/K) + (1/M) = 1/16
Work done by Raja, kundan and Mahesh in one day = (1/R) + (1/K) + (1/M) = 1/16


3.
We can write, (256)^47 = (16^2)^47 = 16^94
Now, when 16 is divided by 15, the remainder is 1
∴ When 16^94 is divided by 15, the remainder is 1
 
4.
Time taken by train to reach B from A = 11/2 hours
Distance travelled by the train = Speed × Time
∴ Distance travelled by the train = 30 × 11/2 = 165 km


5.
Given that,
S.I = 5/9 P
We know that,
S.I = (P × R × T)/100
⇒ 5/9P = (P × R × 25)/100
⇒ 5/9 × 4 = R
∴ R = 20/9%


6.
 
Simple multiplication 3 × 25 = 75. Bracket takes priority over division, multiplication, addition or subtraction.
Hence, (3 × 25 ) ÷ 5 - 20 × 4 + 75 = 75 ÷ 5 - 20 × 4 + 75 = 15 - 20 × 4 + 75.
Multiplication takes priority over addition or subtraction.
Hence, 15 - 20 × 4 + 75 = 15 - 80 + 75.
Addition takes priority over subtraction.
Hence, 15 - 80 + 75 = 90 - 80 = 10


7.
 
Let Mohit’s original salary be 100
Rahul’s original salary (being 40% more than Mohit’s salary) = 100 + (40% of 100) = 100 + 40 = 140
If Rahul’s salary is now increased by 60%, then Rahul’s new salary = 140 + (60% of 140) = 140 + 84 = 224
If Mohit’s salary is decreased by 20%, then Mohit’s new salary = 100 - (20% of 100) = 100 - 20 = 80
To find Rahul’s salary is how much percentage of Mohit’s salary
⇒ 224 = ? % of 80
⇒ ? = (224/80) × 100% = 2.8 × 100% = 280%
∴ Required Percentage = 280%
8.
 
Let the C. P. of the article be Rs. xx
According to question,
425 - x = x – 355
2x = 425 + 355 = 780
x  = 780/2
x = 390


9.
 
Let the cost price of each book be Rs. 1.
C. P. of 20 books = Rs. 20
S.P. of 20 books = C. P. of 25 books = Rs. 25
Profit percent =[25−20]/20 × 100 = 25%


10.
∵ Average weight of P and Q is 32 kg
⇒ Sum of their weight = 2 × 32 = 64
⇒ P + Q = 64 kg (1)
Similarly,
Q + R = 86 kg (2)
P + R = 102 kg (3)
Adding equation (1), (2) and (3)
2P + 2Q + 2R = 64 + 86 + 102 = 252
⇒ P + Q + R = 126 kg
∴ Average weight of P, Q and R = (P + Q + R)/3 = 126/3 = 42 kg