Percentage - Study Mode

[#296] In a certain organisation, 40% employees are matriculates, 50% of the remaining are graduates and the remaining 180 are post-graduates. What is the number of graduate employees ?
Correct Answer

(A) 180

Explanation

Solution: Let the total number of employees be x Then, (100 - 50)% of (100 - 40)% of x = 180 50% of 60% of x = 180 $$eqalign{
& Rightarrow left( {frac{{50}}{{100}} imes frac{{60}}{{100}} imes x}
ight) = 180 cr
& Rightarrow x = left( {frac{{180 imes 10}}{3}}
ight) cr
& Rightarrow x = 600 cr} $$ ∴ Number of graduate employees : $$=$$ 50% of 60% of x $$eqalign{
& = left( {frac{{50}}{{100}} imes frac{{60}}{{100}} imes 600}
ight) cr
& = 180 cr} $$

[#297] In an examination in which full marks were 800, A gets 20% more than B, B gets 20% more than C, and C gets 15% less than D. If A got 576, what percentage of full marks did D get (approximately) ?
Correct Answer

(C) 58.82

Explanation

Solution: $$eqalign{
& A = frac{{120}}{{100}}B, cr
& B = frac{{120}}{{100}}C, & cr
& C = frac{{85}}{{100}}D cr
& herefore B = frac{5}{6}A cr
& C = frac{5}{6}B, & cr
& D = frac{{20}}{{17}}C cr
& B = frac{5}{6} imes 576 = 480 cr
& C = frac{5}{6} imes 480 = 400 cr
& D = frac{{20}}{{17}} imes 400 = frac{{8000}}{{17}} cr} $$ So, required percentage : $$eqalign{
& = left( {frac{{8000}}{{17}} imes frac{1}{{800}} imes 100}
ight)\% cr
& = 58.82\% cr} $$

[#298] The price of an article is reduced by 25%. In order to retain the original price, the present price has to be increased by :
Correct Answer

(C) 33$$frac{1}{3}$$%

Explanation

Solution: Let the original price = Rs. 100 New price = Rs. 75 Increase on 75 = 25 Increase on 100 : $$eqalign{
& = left( {frac{{25}}{{75}} imes 100}
ight)\% cr
& = frac{{100}}{3}\% cr
& = 33frac{1}{3}\% cr} $$

[#299] A person's salary is decreased by steps of 20%, 15% and 10%. Approximately by what percent should the reduced salary be increases so as to get back the original salary ?
Correct Answer

(D) 63%

Explanation

Solution: Let original salary = Rs. 100 New salary : 90% of 85% of 80% of Rs. 100 $$eqalign{
& = { ext{Rs}}{ ext{.}}left( {frac{{90}}{{100}} imes frac{{85}}{{100}} imes frac{{80}}{{100}} imes 100}
ight) cr
& = { ext{Rs}}{ ext{.}}frac{{306}}{5} cr} $$ Increase on $$frac{{306}}{5}$$ : = $$left( {100 - frac{{306}}{5}}
ight)$$ = $$frac{194}{5}$$ Increase on 100 : $$eqalign{
& = left( {frac{{194}}{5} imes frac{5}{{306}} imes 100}
ight)\% cr
& = frac{{9700}}{{153}}\% . cr
& = 63.39 approx 63\% cr} $$

[#300] A building worth Rs. 133100 is constructed on land worth Rs. 72900. After how many years will the value of both be the same if land appreciates at 10% p.a. and building depreciates at 10% p.a. ?
Correct Answer

(D) 3

Explanation

Solution: Let the required time be n years Then, $$ Leftrightarrow 72900 imes {left( {1 + frac{{10}}{{100}}}
ight)^n} = $$ xa0 xa0 xa0$$133100 , imes $$ xa0$${left( {1 - frac{{10}}{{100}}}
ight)^n}$$ $$eqalign{
& Leftrightarrow {left( {frac{{11}}{{10}}}
ight)^n} imes {left( {frac{{10}}{9}}
ight)^n} = frac{{133100}}{{72900}} cr
& Leftrightarrow {left( {frac{{11}}{9}}
ight)^n} = frac{{1331}}{{729}} cr
& Leftrightarrow {left( {frac{{11}}{9}}
ight)^n} = {left( {frac{{11}}{9}}
ight)^3} cr
& Leftrightarrow n = 3 cr} $$