7. 1500 is increased by 20%. Find the final number.
a. 1000
b. 1500
c. 1800
d. 2500
Answer: C
Explanation:
Final number $ = 1500\left( {1 + \dfrac{{20}}{{100}}} \right)$$ = 1500\left( {\dfrac{{120}}{{100}}} \right) = 1800$
Alternative method 1:
If the original number is 100%, then after 20% increment it becomes 120% .
Final number = 1500 × 120% = $1500 \times \left( {\dfrac{{120}}{{100}}} \right) = 1800$
Alternative method 2:
Final number = Initial number + 20%(original number) $= 1500 + 20\%(1500)$ $= 1500 + 300 = 1800$.
8. 2000 is decreased by 30%. Find the final number.
a. 1100
b. 1200
c. 1300
d. 1400
Answer: D
Explanation:
Final number $ = 2000\left( {1 - \dfrac{{30}}{{100}}} \right)$$ = 2000\left( {\dfrac{{70}}{{100}}} \right) = 1400$
Alternative method 1:
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 2:
Final number = Initial number - 30%(original number) $= 2000 - 30\%(2000)$ $= 2000 - 600 = 1400$.
9. A number when increased by 25% became 150. Find the original number.
a. 80
b. 100
c. 120
d. 140
Answer: C
Explanation:
Let the original number be $=x$
$ \Rightarrow x\left( {1 + \dfrac{{25}}{{100}}} \right) = 150$
$ \Rightarrow x\left( {\dfrac{{125}}{{100}}} \right) = 150$
$ \Rightarrow x = 150 \times \dfrac{{100}}{{125}}$
$ \Rightarrow x = 120$
Alternative method:
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 = $\dfrac{{150}}{{125\% }} = \dfrac{{150}}{{\left( {\dfrac{{125}}{{100}}} \right)}}$ = $150 \times \dfrac{{100}}{{125}} = 120$
10. A number when decreased by 10% became 450. Find the original number.
a. 350
b. 400
c. 500
d. 700
Answer: C
Explanation:
Let the original number be $=x$
$ \Rightarrow x\left( {1 - \dfrac{{10}}{{100}}} \right) = 450$
$ \Rightarrow x\left( {\dfrac{{90}}{{100}}} \right) = 450$
$ \Rightarrow x = 450 \times \dfrac{{100}}{{90}} = 500$
Alternative method:
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 = $\dfrac{{450}}{{90\% }} = \dfrac{{450}}{{\left( {\dfrac{{90}}{{100}}} \right)}}$ = $450 \times \dfrac{{100}}{{90}} = 500$
11. 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. 1000
b. 1200
c. 1500
d. 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 = $240 \times \dfrac{{100}}{{20}} = 1200$
12. 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
