31. A student who secures 20% marks in an examination fails by 30 marks. Another student who secures 32% marks gets 42 marks more than those required to pass. The percentage of marks required to pass is :
a. 20
b. 25
c. 28
d. 30

Answer: B

Explanation:
Let the pass mark is P. Then P = 20% of x+30 Also P = 32% of x-42
Equating both,
20% of x + 30 = 32% of x - 42
or 12% of x=72. So x=$\displaystyle\frac{{72 \times 100}}{{12}} = 600$
Pass marks = 20% of 600 + 30=150
Pass percentage = $\left( {\displaystyle\frac{{150}}{{600}} \times 100} \right)$% = 25%

32. 5% Income of A is equal to 15% Income of B and 10% Income of B is equal to 20% Income of C. If income of C is Rs.2000, then total income of A, B and C is :
a. Rs.6000
b. Rs.18000
c. Rs.20000
d. Rs.14000

Answer: B

Explanation:
5% A = 15% B and 10% B = 20% C
$\displaystyle\frac{A}{{20}} = \displaystyle\frac{{3B}}{{20}}$ and $\displaystyle\frac{B}{{10}} = \displaystyle\frac{C}{5}$ or B = 2C
$\displaystyle\frac{A}{{20}} = \displaystyle\frac{3}{{20}} \times 2C = \displaystyle\frac{3}{{10}}C$
=$\displaystyle\frac{3}{{10}} \times 2000 = 600$
A = $(600 \times 20) = 12000$
B = $(2 \times 2000) = 4000$
A + B + C = (12000 + 4000 + 2000) = 18000

Alternatively:
You can solve this question by calculating B's income from C's and then A's

33. In mathematics exam a student secured 30% marks in the first paper out of a total of 180. How much should he score in second paper out of a total of 150, If he is to get an over all average of at least 50% ?
a. 74%
b. 76%
c. 70%
d. 80%

Answer: A

Explanation:
30% of 180 + x% of 150 = 50% of (180+150)
or 54 + $\displaystyle\frac{x}{{100}} \times 150 = 165$ or $\displaystyle\frac{{3x}}{2} = 111$
or x = $\displaystyle\frac{{111 \times 2}}{3} = 74$

34. 75% of a number when added to 75, is equal to a number. The number is :
a. 150
b. 200
c. 225
d. 300

Answer: D

Explanation:
75 + 75% of x = x
$75 + \displaystyle\frac{3}{4}x = x \Rightarrow \displaystyle\frac{1}{4}x = 75$
x=$75 \times 4 = 300$

35. After spending 40% in machinery, 25% in building, 15% in raw material and 5% on furniture, Harilal had a balance of Rs.1305. The money with him was :
a. Rs.6500
b. Rs.7225
c. Rs.8700
d. Rs.1390

Answer: C

Explanation:
x - (40% of x + 25% of x + 15% of x + 5% of x) = 1305
x - 85% of x = 1305
15% of x = 1305
x = $\displaystyle\frac{{1305\times100}}{{15}} = 8700$

36. A man donated 5% of his income to a charitable organisation and deposited 20% of the remainder in a bank. If he now has Rs.1919 left, what is his income ?
a. Rs.2558.60
b. Rs.2525
c. Rs.2500
d. Rs.2300

Answer: B

Explanation:
Let his income be Rs.100x . Then, donation = 5% (100x) = 5x.
Remaining amount = 100x - 5x = 95x
Deposited money = 20% (95x) = 1/5 (95x) = 19x
So remaining money = 95x - 19x = 76x
But given that 76x = 1919 $ \Rightarrow x = \displaystyle\frac{{1919}}{{74}} = \displaystyle\frac{{101}}{4}$
So his income = 100x = $\displaystyle\frac{{101}}{4} \times 100 = 2525$