Quant Quiz

Question.1. Vandana’s salary become equal to 15/8 times of his initial salary if she After receives two successive raises.if the second raise was twice as high (in percent) as the first raises then find the percent of salary raised the first time ?
1) 23.76%
2) 32.45%
3) 25.00%
4) 18.75%
5) 43.34%

Question.2. A Merchant gives 3 consecutive discounts of 10%. 15% and 15% after which he sells his goods at a percentage profit of 30.05% on the C.P. Find the value of the percentage profit that the shopkeeper would have earned if he had given discount of 10% and 15% only.
1) 53.00%
2) 42.75%
3) 62.35%
4) 84.46%
5) 56.24%

Question.3. A sum of Rs. 1000 after 3 years at compound interest becomes a certain amount that is equal to the amount that is the result of a 3 year depreciation from Rs. 1728. Find the difference between the rates of CI and depreciation. (Given CI is 10% p.a.)
1) 6.53%
2) 5.86%
3) 4.58%
4) 3.23%
5) 1.67%

Question.4. A Boat travelling at the somespeed, can cover 25 km upstream and 39 km downstream in 8 h. At the same speed, it can travel 35 km upstream and 52 km downstream in 11 h. The speed of the boat is
(a) 8.5 km/h
(b) 6.0 km/hr
(c) 9.0 km/h
(d) 12.0 km/h
(e) None of the above

Question.5. A box contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the box, the probability that it is green is 2/3. The number of blue balls in the box is
(a) 10
(b) 20
(c) 12
(d) 8
(e) None of the above

Question.6. If the sum of the lengths of the diagonals of a rhombus is 10 m and if its area is 9 m^2. Then, what is the sum of squares of the diagonals?
(a) 76 m^2
(b) 64 m^2
(c) 38 m^2
(d) 90 m^2
(e) None of the above

Question.7. Circumference of a circle A is 1(4/7) times perimeter of a square. Area of the square is 784 sq cm. What is the area of another circle B whose diameter is half the radius of the circle A?
(a) 154.00 sq cm
(b) 216.32 sq cm
(c) 365.18 sq cm
(d) 346.86 sq cm
(e) None of the above

Question.8. Floor of a square room of side 10 m is to be completed covered with square tiles, each having length 50 cm. The smallest number of tiles needed is 
(a) 300
(b) 250
(c) 400
(d) 600
(e) None of these

Question.9. The ratio of 1st and 2nd classes of Bus fairs between two cities is 3 : 1 and that of the number of passengers travelling between these cities by 1st and 2nd classes is 1 : 50. If on a particular day, Rs. 2650 be collected from the passengers travelling between these cities, then find the amount collected from 2nd class passengers.
(a) Rs. 5605
(b) Rs. 4300
(c) Rs. 3840
(d) Rs. 2500
(e) None of these

Question.10. Roshani scores 80% marks in five subjects together, viz., english, art, literature, hindi and Urdu, where in the maximum marks of each subject were 105. How many marks did Roshani score in Art, if she scored 89 marks in English, 92 marks in Urdu, 98 marks in Literature and 81 marks in Hindi?
(a) 60
(b) 65
(c) 85
(d) 74
(e) None of the above.

Solutions:

1.(c)
Let the rate of salary raised was r% and initial salary was ‘X’ Rs. 
X*[(100- r)/100]*[(100+2r)= (15/8)*X
:. 10000 + 200r + 100r + 2r^2 = (15/8)*100*100
:. 2r^2 + 300r + 10000 – 18750 = 0 
or, 2r^2 + 300r – 8750 = 0 
:. r^2+ 150r – 4375 =0 
or, (r + 175)(r – 25) = 0
hence, rate of salary increased = 25%

2.(a) 
Let marked price= x 
Now, selling price= x*[(100-10)/100]*[(100-15)/100]^2
Selling price= [(90 x 85 x 85)/(100 x 100 x 100)]*x = 0.65025*x Profit % = 30.05 = [(SP- CP)/CP]*100
[0.65025*x – CP)/CP]*100 = 30.05 
therefore,
0.3005 CP + CP = 0.65025*x
hence, Cost price = (0.65025/1.3005)*x = 0.5 *x
Now, 
new selling price, when only 10% and 15% discount is given. 
Then selling price= x*(90/100)*(85/100)= 0.765*x 
New Profit%= [(0.765*x – 0.5*x)/0.5*x]x 100= 53%

3.(5); 
Since, Amount after 3 years @ 10 % per annum = 1000x(1+(10/100))^3 = 1000x(1331/1000)= 1331 Rs. 
Now, Let R% is depreciation Rate 
:.1728x(1-(R/100))^3= 1331
or,
(1-(R/100))^3= (1331/1728)= (11/12)^3
hence,
1 – (R/100)= 11/12
R = 100/12 = 8.33% (Rate of depreciation)
hence required Difference in Rates=10-8.33= 1.67%

4. (c); Let the speed of a boat & stream be x & y kmph.
According to question
25/(x-y)+39/(x+y)=8 …………(i)
&
35/(x-y)+52/(x+y)=11………..(ii)
From (i) and (ii)
x=9, y=4
Hence speed of stream, y=4

5.(d); 
Let the number of green marble=x
So, xC1/24C1=2/3
x=16
So, No. of blue marble=24-16=8

6.(b); 
Let diagonals of rhombus be x & y.
Given x+y=10
Area of rhombus= (1/2)* x*y= 9
xy=18
x^2+y^2=(x+y)^2-2xy
=(10)^2-2.18
=(10)^2-2.18
=64

7.(a); 
Side of square=(784)^(1/2)=28
2pi R=(11/4)X4X28
R=28
Diameter of another circle B=1/2 R=(1/2)X28=14
r=14/2=7
Area of circle=B=pi*7^2=154 cm^2

8.(c); 
Number of tiles needed=(Area of square room)/(Area of tile)
=(10X100X10X100)/(50X50)
=400

9.(d); 
Ratio of the amount collected from 1st& 2nd class fairs=(3X1): (1X50)= 3 : 50
Required Amount=2650X(50/53)=2500
10.(a); 
80% of total marks=80%of(105X5)= 420
So, obtained marks in Art= 420-(89+92+98+81)=60