Maths Quiz for KVS/NVS PGT Exams



Q1. A dishonest dealer professes to sell at cost price but uses a 900 gram weight instead of 1-kilogram weight. Find the percent profit to the dealer.
(a) 11.11%
(b) 14%
(c) 12.13%
(d) 15%
Sol.
Let the cost price be x Rs. per kg.
Then cost price of 900 gn =9/10 x
Hence % profit
=(x – 9/10 x)/(9/10 x)×100=100/9%=11.11%

Q2. The Average age of a class of 22 students is 21 years. The average increased by 1 when the teacher’s age also included. What is the age of the teacher?
(a) 48
(b) 45
(c) 43
(d) 44
Sol.
Total age of all students = 22×21
Total age of all students + age of the teacher = 23 × 22
Age of the teacher = 23×22 – 22×21 = 22(23-21) = 22×2 = 44

Q3.My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then what was the age my father when my brother was born?
(a) 35 years
(b) 34 years
(c) 33 years
(d) 32 years
Sol.
Let my age = x
My mother’s age = x + 26
My sister’s age = (x + 3) + 4 = x + 7
My Father’s age = (x + 7) + 28 = x + 35
=> age my father when my brother was born
= x + 35 – (x + 3) = 32

Q4. The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
(a) 8, 20, 28
(b) 16, 28, 36
(c) 20, 35, 45
(d) None of these
Sol.
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x – 8) + (7x – 8) + (9x – 8) = 56
=>  20x = 80
=>  x = 4.
So  Their present ages are 4x = 16 years,
7x = 28 years and 9x = 36 years respectively.

Q5.The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person?
(a) 10
(b) 20
(c) 30
(d) 40
Sol.
Let’s take the present age of the elder person = x and the present age of the younger person
= x – 16
(x – 6) = 3 (x-16-6)
=> x – 6 = 3x – 66
=> 2x = 60
=> x = 60/2 = 30

Q6. Mr. Ravi spent 20% of his monthly income on food and 15% on children’s education, 40% of the remaining he spent on entertainment and transport together and 30% on medical. He is left with an amount Rs. 8775 after all these expenditures. What is Mr. Ravi’s monthly income?
(a) Rs. 40,000
(b) Rs. 35,000
(c) Rs. 45,000
(d) Rs. 38,000
Sol.
let total monthly income of ravi  =X
X of 30% of 65% = 8775 ⇒
=(8775 × 100 × 100)/(30 × 65)= Rs. 45,000

Q7. In a class of 35 students and 6 teachers, each student got toffees that are 20% of the total number of students and each teacher got toffees that are 40% of the total number of students. How many toffees were there?
(a) 245
(b) 161
(c) 406
(d) 329
Sol.
35 × 20% of 35 + 6 × 40% of 35
245 + 84 = 329

Q8. If the height of a cylinder is increased by 15% and the radius of its base is decreased by 10%, then by what percent will its curved surface area change?
(a) 3.5% decrease
(b) 3.5% increase
(c) 5% increase
(d) 5% decrease
Sol.
H1=100   H2=115
R1=100   R2=90
Curved surface area =πrh
π R1  H1   π R2  H2
⇒ 100 × 100  ⇒ 115 × 90
⇒ 10,000  ⇒ 10350
⇒ 200   ⇒ 207
Increase = 207 – 200 = 7
% increase =increase/original×100%
=7/200×100=3.5%

Q9. A house and a shop were sold for Rs. 1 lakh each. In this transaction, the house sale resulted into 20% loss whereas the shop sale resulted into 20% profit.The entire transaction resulted in
(a) No loss no gain
(b) Gain of Rs. 1/24 lakh
(c) Loss of Rs. 1/12 lakh
(d) Loss of Rs. 1/18 lakh
Sol.
Total S.P. = Rs. 2 lakhs
C.P. =100/(100 –  L%)×S.P.
C.P of house = Rs. (100/80×1) lakh
= Rs. 5/4 lakh
C.P. =(100 )/(100-P%)×S.P.
C.P. of shop =Rs.(100/120×1) lakh =Rs.5/6
Total C.P. = Rs. (5/4+5/6) lakhs
= Rs. 25/12 lakhs
∴ Loss = Rs. (25/12-2) lakh = Rs. 1/12 lakh

Q10. A ruby stone was bought for Rs.1600 at Jaipur. A sum of Rs.2400 was spent on making a ring with the ruby stone. It was advertised for sale of Bombay for Rs.7800. If a discount of 10% was given, then the percentage profit made was:
(a) 55%
(b) 68.5%
(c) 75.5%
(d) 80%
Sol.
cost price of Rubi stone = Rs.1600
cost price of Ring = Rs.2400
Actual cost price = Rs. 4000
Selling price = (7800*90/100)= 7020
profit percent = (7020-4000)/4000 *100=75.5%