QUANTITATIVE APTITUDE - 21

1. The respective ratio of the number of boys to the number of girls studying in a school is 25 : 29. The total number of students studying in the school is 270. If 15 boys and 15 girls take admission in the school. What will be the new respective ratio of the boys and girls studying in the school?
a) 6 : 7
b) 8 : 9
c) 7 : 8
d) 7 : 9
e) None of these

2. The profit earned after selling a T-shirt for Rs.575 is the same as loss incurred after selling the same T-shirt for Rs.295. What is the cost price of the T-shirt?
a) 425
b) 445
c) 430
d) 450
e) None of these

3. In a class of 125 students 20% of the students can dance 2/5 th of the total number of students in the class can sing and 2/5 th of the remaining number of students in the class are good at sports. What is the respective ratio of the number of students who can dance to the number of students who are good at sports?
a) 5 : 4
b) 4 : 3
c) 5 : 3
d) 6 : 2
e) None of these

4. Amrita took a loan of Rs.50600 at a certain rate of simple interest for 5yr. At the end of 5yr, she repayed an amount of Rs.65780. What is the rate of interest at which Amrita took the loan?
a) 5%/annum
b) 4%/annum
c) 8%/annum
d) 6%/annum
e) None of these

5. The population of a town two years ago was 45000. It increased by 12% in the first year and decreased by 15% in the second year. What was the population of the town at the end of two years.
a) 57960
b) 42840
c) 44820
d) 50400
e) None of these

6. The respective ratio of the length and breadth of a rectangular plot is 3 : 2. If the length of the plot is 40m more than its breadth, what is the perimeter of the rectangular plot?
a) 200m
b) 400m
c) 500m
d) Can't be determined
e) None of these

Directions (Q.6 - 10): In the following number series only one number is wrong. Find out the wrong number.

7. 3,  7,  16,  35,  72,  153,  312
a) 7
b) 153
c) 35
d) 72
e) 16

8. 18,  20,  23,  32,  48,  73,  109
a) 20
b) 23
c) 32
d) 48
e) 73

9. 7,  4,  5,  9,  20,  51,  160.5
a) 4
b) 5
c) 9
d) 20
e) 51

10. 6,  10,  14,  34,  66,  130,  258
a) 10
b) 14
c) 34
d) 66
e) 130

Answers: 

1. c) Number of boys = 25/(25+29) * 270 = 125
No. of girls = 270 - 125 = 145
No. of new boys = 125 + 15 = 140
No. of new girls = 145 + 15 = 160
Hence, new ratio = 140/160 = 7 : 8.

2. e) Suppose cost price of T-shirt is Rs.X
Then, 575 - X = X - 295 => 2X = 870 => X = 435.

3. a) Number of dance students = 125 * 20/100 = 25
No. of students who can sing = 125 * 2/5 = 50
Remaining no. of students = 125 - (25+50) = 50
No. of students good at sports = 50 * 2/5 = 20
Hence, rewuired ratio = 25/20 = 5/4 = 5 : 4.

4. d) SI for 5yr = 65780 - 50600 = 15180
We know that, SI = PRT/100
=> 15180 = (50600*r*5)/100 => r = (15180*100)/(50600*5) = 6%.

5. b) The population of the town at the end of two years,
= 45000 * (1 + 12/100) (1 - 15/100) = 45000 * 28/25 * 17/20 = 42840.

6. b) Let the length and breadth of the rectangular plot be 3X and 2X m respectively.
Then, 3X - 2X = 40 => X = 40m
hence, perimeter of the rectangular plot = 2( L + B)
= 2( 3X + 2X ) = 10X = 400m.

7. 4) 72 wrong number. 
Pattern is = *2 + 1, *2 + 2, *2 + 3, *2 + 4, *2 + 5, *2 + 6.

8. a) 20 wrong number.
pattern is = +(1)^2, +(2)^2, +(3)^2, +(4)^2 ...

9. e) 51 wrong number.
Pattern is = *0.5 + 0.5, *1 + 1, *1.5 + 1.5, *2 + 2, *2.5 + 2.5, *3 + 3.

10. b) 14 wrong number.
Pattern is = *2 - 2, *2 - 2, *2 - 2, *2 - 2 ...