1. 1500 is increased by 20%. Find the final number.
a. 1000
b. 1500
c. 1800
d. 2500

Answer: C

Explanation:
If the original number is 100%, then after 20% increment it becomes 120% .
Final number = 1500 × 120% = $1500 \times \left( {\dfrac{{120}}{{100}}} \right) = 1800$

Alternative method:
Final number = Initial number + 20%(original number) = 1500 + 20%(1500) = 1500 + 300 = 1800.

2. 2000 is decreased by 30%. Find the final number.
a. 1100
b. 1200
c. 1300
d. 1400

Answer: D

Explanation:
If the original number is 100%, then after 30% decrement it becomes 70% .
Final number = 2000 × 70% = $2000 \times \left( {\dfrac{{70}}{{100}}} \right) = 1400$

Alternative method:
Final number = Initial number - 30%(original number) = 2000 - 30%(2000) = 2000 - 600 = 1400.

3. A number when increased by 25% became 150. Find the original number.
a. 80
b. 100
c. 120
d. 140

Answer: C

Explanation:
To increase the original number by 25%, we need to multiply the original number by (100 + 25) % or 125%.
Original number × 125% = 150 $ \Rightarrow $ Original number = $\dfrac{{150}}{{125\% }} = \dfrac{{150}}{{\left( {\dfrac{{125}}{{100}}} \right)}}$ = $150 \times \dfrac{{100}}{{125}} = 120$

4. A number when decreased by 10% became 450. Find the original number.
a. 350
b. 400
c. 500
d. 700

Answer: C

Explanation:
To decrease the original number by 10%, we need to multiply the original number by (100 - 10)% or 90%.
Original number × 90% = 450 $ \Rightarrow $ Original number = $\dfrac{{450}}{{90\% }} = \dfrac{{450}}{{\left( {\dfrac{{90}}{{100}}} \right)}}$ = $450 \times \dfrac{{100}}{{90}} = 500$

5. In an election contest between A and B, A wins by the margin of 240 votes. If A gets 60% of the total votes, total votes are:
a. Rs.1000
b. Rs.1200
c. Rs.1500
d. Rs.2000

Answer: B

Explanation:
Votes casted in favour of A = 60%
Votes casted in favour of B = (100 - 60)% = 40%
Therefore, A wins by (60% - 40%) = 20% of the total votes.
$ \Rightarrow $ 20% (Total votes) = 240
$ \Rightarrow \dfrac{{20}}{{100}}$(Total votes) = 240
Total votes = $240 \times \dfrac{{100}}{{20}} = 1200$

6. A student has to secure 40% marks in an examination to qualify. He gets 120 marks and fails by 80 marks. The maximum marks are
a. 450
b. 500
c. 600
d. 650

Answer: B

Explanation:
Passing marks = 120 + 80 = 200
$ \Rightarrow $ 40% of the maximum marks = 200
$ \Rightarrow $ Maximum marks = $\dfrac{{200}}{{40\% }} = 200 \times \dfrac{{100}}{{40}}$ = 500

7. A student got 42% marks and has secured 12 marks more than the minimum passing marks. Another student got 45% has obtained 30 marks more than the minimum passing marks. The maximum marks are:
a. 1200
b. 900
c. 600
d. 800

Answer: C

Explanation:
Let the maximum mark = m, and pass mark = p.
Marks secured by first student = 42%(m) = p + 12
Marks secured by second student = 45%(m) = p + 30
Subtracting the first from the second, 3%(m) = 18
$ \Rightarrow $ m = $18 \times \dfrac{{100}}{3} = 600$

Alternative method:
Difference in percentage of marks = 45% - 42% = 3%
Difference in marks = 30 - 12 = 18 (i.e. 6 times of 3)
Therefore, Maximum marks = 6 x 100 = 600

8. A person saves 10% of his income. If his income is increased by 20% and he saves 15% of the new income, by what percent his savings will increase?
a. 80%
b. 60%
c. 50%
d. 40%

Answer: A

Explanation:
Let previous income = Rs. 100
Previous savings = 10% of Rs. 100 = Rs. 10
Increased income = Rs. 100 + 20% of Rs. 100 = Rs. 120
Increased savings = 15% of Rs. 120 = Rs. 18
Therefore, Increase in savings = Rs. 18 - Rs. 10 = Rs. 8
Therefore, Percent increase in savings = $\displaystyle\frac{{\rm{8}}}{{{\rm{10}}}}$ x 100 = 80%