Percentage - Study Mode

[#271] Aman's expense is 30% more than Vimal's and Vimal's expense is 10% less than Raman's. If the sum of their expenses is Rs. 6447, then what would be Aman's expense ?
Correct Answer

(D) Rs. 2457

Explanation

Solution: Let Raman's expense be Rs. $$x$$ Then, Vimal's expenses : = 90% of $$x$$ $$eqalign{
& = { ext{ Rs}}{ ext{. }}left( {frac{{90}}{{100}} imes x}
ight) cr
& = { ext{Rs}}{ ext{. }}frac{9}{{10}}x{ ext{ }} cr} $$ Aman's expense : $$eqalign{
& = { ext{130% of Rs}}{ ext{. }}left( {frac{{9x}}{{10}}}
ight) cr
& = { ext{ Rs}}{ ext{. }}left( {frac{{130}}{{100}} imes frac{{9x}}{{10}}}
ight) cr
& = { ext{ Rs}}{ ext{. }}frac{{117x}}{{100}} cr
& herefore frac{{117x}}{{100}} + frac{{9x}}{{10}} + x = 6447 cr
& Rightarrow frac{{117x + 90x + 100x}}{{100}} = 6447 cr
& Rightarrow 307x = 644700 cr
& Rightarrow x = frac{{644700}}{{307}} cr
& Rightarrow x = 2100 cr
& { ext{Hence, Aman's expenses :}} cr
& = { ext{Rs}}{ ext{. }}left( {frac{{117 imes 2100}}{{100}}}
ight) cr
& = { ext{Rs}}{ ext{. 2457}} cr} $$

[#272] If A is 150 percent of B, then B is what percent of (A + B) ?
Correct Answer

(B) $$40\% $$

Explanation

Solution: $$eqalign{
& A = 150\% { ext{ of }}B cr
& Rightarrow A = frac{{150}}{{100}}B cr
& Rightarrow frac{A}{B} = frac{3}{2} cr
& Rightarrow frac{A}{B} + 1 = frac{3}{2} + 1 cr
& Rightarrow frac{{A + B}}{B} = frac{5}{2} cr
& Rightarrow frac{B}{{A + B}} = frac{2}{5} cr} $$ ∴ Required percentage : $$eqalign{
& = left( {frac{B}{{A + B}} imes 100}
ight)\% cr
& = left( {frac{2}{5} imes 100}
ight)\% cr
& = 40\% cr} $$

[#273] From the salary of an officer, 10% is deducted as house rent, 20% of the rest, he spends on conveyance, 20% of the rest he pays as income tax and 10% of the balance, he spends on clothes. Then, he is left with Rs. 15552. Find his total salary.
Correct Answer

(B) Rs. 30000

Explanation

Solution: Let the total salary be Rs. $$x$$ Then, (100 -10)% of (100 - 20)% of (100 - 20)% of (100 - 10)% of $$x$$ = 15552 $$ Leftrightarrow left( {frac{{90}}{{100}} imes frac{{80}}{{100}} imes frac{{80}}{{100}} imes frac{{90}}{{100}} imes x}
ight)$$ xa0 xa0 xa0 $$ = 15552$$ $$eqalign{
& Leftrightarrow x = left( {frac{{15552 imes 10000}}{{64 imes 81}}}
ight) cr
& Leftrightarrow x = 30000 cr} $$

[#274] In an examination, 35% candidates failed in one subject and 42% failed in another subject while 15% failed in both the subjects. If 2500 candidates appeared at the examination, how many passed in either subject but not in both ?
Correct Answer

(B) 1175

Explanation

Solution: Failed in 1 st subject = $$frac{35}{100}$$ × 2500 = 875 Failed in 2 nd subject = $$frac{42}{100}$$ × 2500 = 1050 Failed in both = $$frac{15}{100}$$ × 2500 = 375 Failed in 1 st subject only = (875 - 375) = 500 Failed in 2 nd subject only = (1050 - 375) = 675 ∴ Passed in 2 nd only + Passed in 1 st only = (675 + 500) = 1175

[#275] 14% of 14 + 28% of 28 + 92% of 96 - 15% of 85 = ?
Correct Answer

(B) 85.37

Explanation

Solution: It is given that, (14% of 14) + (28% of 28) + (92% of 96) - (15% of 85) = ? $$left( ?
ight) = left( {frac{{14 imes 14}}{{100}}}
ight) + left( {frac{{28 imes 28}}{{100}}}
ight) + $$ xa0 xa0 xa0 $$left( {frac{{92 imes 96}}{{100}}}
ight) - left( {frac{{15 imes 85}}{{100}}}
ight)$$ $$eqalign{
& left( ?
ight) = left( {1.96 + 7.84 + 88.32 - 12.75}
ight) cr
& left( ?
ight) = left( {98.12 - 12.75}
ight) cr
& left( ?
ight) = 85.37 cr} $$