Maths Quiz for 2016-17 Exams

Q1. Two numbers are respectively 19% and 70% more than a third number. What percentage is the first number out of the second?  
(a) 70
(b) 50
(c) 90
(d) 80
Sol.
Let the third number be 100.
Then, the first number is 100 + 19 = 119 and the second number is 170.
∴ The first is 119/170×100=70% of the second.

Q2. 20% of the populations in a town are females. If there are 72,000 males, how many females are there?  If there are no eunuchs in the town.
(a) 14400
(b) 27000
(c) 36000
(d) 18000
Sol.
Let the total population in town = 100x
Male population = 80x
Female population = 20x
So, total female population =72000/4=18000

Q3. Mr Moron calculates his profit percentage as a percentage on selling price. He sells an item for Rs. 150 and calculates his profit percentage to be 20%. What is the true profit percentage?
(a) 15%
(b) 20%
(c) 25%
(d) 35%
Sol.
Sell price = 150
Profit =20/100×150 (According to question)
= 30 rupees
So cost profit = 150 – 30 = 120 rupees
True profit % =(Profit )/(Cost price )×100
=30/120×100=25%

Q4. When the selling price of a watch is Rs. 130, the loss percentage is 25%. What is the loss or gain percentage if selling price is increased to Rs. 182?
(a) 10%
(b) 5%
(c) 20%
(d) 16.6%
Sol.
Selling price = 130 rupees
Cost price =130/.75=520/3 rupees
When selling price Rs. 182
Profit % will be =((182 – 520/3 )/(520/3) )  × 100
=(26/520)×100 = 5%

Q5. Profit earned by selling an article for Rs. 1060 is 20% more than the loss incurred by selling the article for Rs. 950. At what price should the article be sold to earn 20% profit?
(a) Rs. 10000
(b) Rs. 12000
(c) Rs. 13000
(d) Rs. 11000
Sol.
Let the C.P of the article is x
According to question,
(1060 – x) = 1.2 × (x – 950)
1060 – x = 1.2x – 1140
1.2x = 1200
x = 1000 ⇒ Cost price = 1000
Required answer, selling price = 1000 × 1.2 = Rs. 12000

Q6. A class has girls and boys in the ratio 4 : 5. Among the girls, the ratio of mathematics to Physics students is 3 : 1. What percentage of the class comprises girls studying Mathematics?
(a) 33.3%
(b) 25%
(c) 20%
(d) 16.6%
Sol.
Let the number of boys and girls in 5x and 4x respectively.
Girls who studying mathematic = 3x
So, required percentage =3x/9x   = 33.3%

Q7. Aditya purchases toffees at Rs. 10 per dozen and sells them at Rs. 12 for every 10 toffees. Find the gain or loss percentage.
(a) 20%
(b) 40%
(c) 24%
(d) 44%
Sol.
Cost price = Rs. 10/12
Selling price = Rs. 12/10
SP/CP=144/100=1.44
Therefore, gain percentage = 44%

Q8. A shopkeeper sells notebooks at the rate of Rs. 45 each and terms a commission of 4%. He also sells pencil box at the rate of Rs. 80 each and earns a commission of 20%. How much amount of commission will he earn in two weeks, if he sells 10 notebooks and 6 pencil boxes a day?
(a) Rs. 1956
(b) Rs. 1586
(c) Rs. 1496
(d) Rs. 1596
Sol.
Notebooks in a day, then in two weeks (i.e. 14 days) = 14 × 10 = 140 notebooks
Commission earned =45×4/100×140 = Rs. 252
6 pencil boxes in a day, then in two weeks (i.e. 14 days) = 14 × 6 = 84 pencil boxes
Commission earned =80×20/100×84 = Rs. 1344
Total commission earned = 252 + 1344 = Rs. 1596

Q9. The cost price of 20 articles is equal to the mark price of 15 articles. If he allowed a 10% discount on a mark price then what is the profit percentage?
(a) 20%
(b) 83%
(c) 23.33%
(d) 25%
Sol.
( mark price)/(cost price )=20/30=4/3
Mark price over the cast price is 33.3%
Profit factor = [(mark price factor) × (Discount factor)] – 1
=4/3×9/10
= 1.2 – 1 = .2
So profit percentage = 20%

Q10. If the difference between the CI and SI earned at the end of second year on a sum of money at the rate of 10% pa is Rs. 20, what was the sum?
(a) Rs 3000
(b) Rs. 2000
(c) Rs. 2500
(d) Rs. 3500
Sol.
Difference between the C.I & S.I for the two year
=P×r/100×r/100
Where r = rate of interest
P = total sum of money
20 × 100 × 100 = P × 10 × 10
P = 2,000