Percentage - Study Mode
[#71] If the price of a book is first decreased by 25% and then increased by 20%, then the net charges in the price will be :
Correct Answer
(D) 10% decrease
Explanation
Solution: Let the original price be Rs. 100 New final price : = 120% of (75% of Rs. 100) = Rs. $$left( {frac{{120}}{{100}} imes frac{{75}}{{100}} imes 100}
ight)$$ = Rs. 90 ∴ Decrease = 10%
[#72] The current birth rate per thousand is 32, whereas the corresponding death rate is 11 per thousand. The net growth rate in terms of population increase in percent is given by :
Correct Answer
(C) 2.1%
Explanation
Solution: Net growth on 1000 $$= (32 - 11)$$ $$= 21$$ Net growth on 100 $$eqalign{
& = left( {frac{{21}}{{1000}} imes 100}
ight)\% cr
& = 2.1\% cr} $$
[#73] A reduction of 21% in the price of wheat enables a person to buy 10.5 kg more for Rs. 100. What is the reduced price per kg ?
Correct Answer
(A) Rs. 2
Explanation
Solution: Let the original price = Rs. $$x$$ per kg Reduced price = Rs. $$left( {frac{{79x}}{{100}}}
ight)$$ per kg $$eqalign{
& herefore frac{{100}}{{79x}} - frac{{100}}{x} = 10.5 cr
& Rightarrow frac{{10000}}{{79x}} - frac{{100}}{x} = 10.5 cr
& Rightarrow 10000 - 7900 = 10.5 imes 79x cr
& Rightarrow x = frac{{2100}}{{10.5 imes 79}} cr} $$ ∴ Reduced price : $$eqalign{
& = { ext{Rs}}{ ext{. }}left( {frac{{79}}{{100}} imes frac{{2100}}{{10.5 imes 79}}}
ight){ ext{ per kg}} cr
& = { ext{Rs}}{ ext{. 2 per kg}} cr} $$
[#74] If X is 90% of Y, then what percent of X is Y ?
Correct Answer
(C) $$111frac{1}{9}\% $$
Explanation
Solution: $$eqalign{
& X = frac{{90}}{{100}}Y cr
& Rightarrow X = frac{9}{{10}}Y cr
& Rightarrow Y = frac{{10}}{9}X cr
& Rightarrow frac{Y}{X} = frac{{10}}{9} cr} $$ ∴ Required percentage : $$eqalign{
& = left( {frac{Y}{X} imes 100}
ight)\% cr
& = left( {frac{{10}}{9} imes 100}
ight)\% cr
& = 111frac{1}{9}\% cr} $$
[#75] 30% apples out of 450 are rotten, How many apples are in good condition ?
Correct Answer
(D) 315
Explanation
Solution: Number of rotten apples : $$eqalign{
& = 30\% { ext{ of }}450 cr
& = left( {frac{{30}}{{100}} imes 450}
ight) cr
& = 135 cr} $$ ∴ Number of good apples = 450 - 135 = 315