Percentage - Study Mode

[#266] Solve this : (23.6% of 1254) - (16.6% of 834) = ?
Correct Answer

(C) 157.5

Explanation

Solution: $$left( {23.6\% { ext{ of 1254}}}
ight) - left( {16.6\% { ext{ of 834}}}
ight)$$ $$ = left( {frac{{236}}{{10}} imes frac{1}{{100}} imes 1254}
ight) - $$ xa0 xa0 $$left( {frac{{166}}{{10}} imes frac{1}{{100}} imes 834}
ight)$$ $$eqalign{
& = frac{1}{{1000}}left( {236 imes 1254 - 166 imes 834}
ight) cr
& = frac{{12}}{{1000}}left( {24662 - 11537}
ight) cr
& = left( {frac{{12 imes 13125}}{{1000}}}
ight) cr
& = 157.5 cr} $$

[#267] One-fourth of sixty percent of a number is equal to two-fifth of twenty percent of another number. What is the respective ratio of the first number to the second number ?
Correct Answer

4 : 7

Explanation

Solution: Let the first number be x and the second number be y $$frac{1}{4}{ ext{ of 60% of }}x = frac{2}{5}{ ext{ of 20% of }}y$$ $$eqalign{
& Rightarrow frac{1}{4} imes frac{{60}}{{100}} imes x = frac{2}{5} imes frac{{20}}{{100}} imes y cr
& Rightarrow frac{{3x}}{{20}} = frac{{2y}}{{25}} cr
& Rightarrow frac{x}{y} = frac{2}{{25}} imes frac{{20}}{3} cr
& Rightarrow frac{x}{y} = frac{8}{{15}} cr} $$

[#268] In an examination, 96% of students passed and 500 students failed. How many students did appear at the examination ?
Correct Answer

(B) 12500

Explanation

Solution: Let number of students who appeared at the examination be $$x$$ Passed percentage = 96% Failed percentage = 4% According to given information we get Unsuccessful students = 4% ∴ 4% of $$x$$ = 500 ⇒ $$left( {frac{{x imes 4}}{{100}}}
ight)$$xa0 = 500 ⇒ $$x$$ = $$left( {frac{{500 imes 100}}{{4}}}
ight)$$ ⇒ $$x$$ = 12500

[#269] The price of a certain item is increased by 15%. If consumer wants to keeps his expenditure on the item same as before, how much percent must he reduce his consumption of that item ?
Correct Answer

(B) $$13frac{1}{{23}}\% $$

Explanation

Solution: Reduction in consumption : $$eqalign{
& = left[ {frac{R}{{left( {100 + R}
ight)}} imes 100}
ight]\% cr
& = left( {frac{{15}}{{115}} imes 100}
ight)\% cr
& = frac{{300}}{{23}}\% cr
& = 13frac{1}{{23}}\% cr} $$

[#270] The difference between 38% of a number and 24% of the same number is Rs. 135.10. What is 40% of that number ?
Correct Answer

(C) 386

Explanation

Solution: Let the number be x Then, $$eqalign{
& 38\% { ext{ of }}x - 24\% ,,{ ext{of }}x = 135.10 cr
& Rightarrow frac{{38}}{{100}}x - frac{{24}}{{100}}x = 135.10 cr
& Rightarrow frac{{14}}{{100}}x = 135.10 cr
& Rightarrow x = left( {frac{{135.10 imes 100}}{{14}}}
ight) cr
& Rightarrow x = 965 cr
& herefore 40\% { ext{ of 965 :}} cr
& = left( {frac{{40}}{{100}} imes 965}
ight) cr
& = 386 cr} $$