Percentage - Study Mode
[#116] If 50% of (x - y) = 30% of (x + y), then what percent of x is y ?
Correct Answer
(A) 25%
Explanation
Solution: $$eqalign{
& 50\% { ext{ of }}left( {x - y}
ight) = 30\% { ext{ of }}left( {x + y}
ight) cr
& Rightarrow 5left( {x - y}
ight) = 3left( {x + y}
ight) cr
& Rightarrow 5x - 5y = 3x + 3y cr
& Rightarrow 2x = 8y cr
& Rightarrow y = frac{x}{4} cr} $$ ∴ Required percentage : $$eqalign{
& = left( {frac{y}{x} imes 100}
ight)\% cr
& = left( {frac{x}{4} imes frac{1}{x} imes 100}
ight)\% cr
& = 25\% cr} $$
[#117] In a History examination, the average for the entire class was 80 marks. If 10% of the students scored 95 marks and 20% scored 90 marks, what was the average marks of the remaining students of the class ?
Correct Answer
(C) 75
Explanation
Solution: Let the number of students in the class be 100 and let the required average be $$x$$ Then, ⇒ (10 × 95) + (20 × 90) + (70 × $$x$$) = (100 × 80) ⇒ 70$$x$$ = 8000 - (950 + 1800) ⇒ 70$$x$$ = 5250 ⇒ $$x$$ = 75
[#118] If (x + 20)% of 250 is 25% more than x% of 220, then 10% of (x + 50) is what percent less than 15% of x?
Correct Answer
(A) $$16frac{2}{3}$$
Explanation
Solution: $$eqalign{
& frac{{250 imes left( {x + 20}
ight)}}{{100}} = frac{{220 imes x}}{{100}} imes frac{{125}}{{100}} cr
& 25x + 500 = 22 imes x imes frac{5}{4} cr
& 100x + 2000 = 110x cr
& 10x = 2000 cr
& x = 200 cr
& frac{{left( {x + 50}
ight) imes 10}}{{100}} = frac{{250 imes 10}}{{100}} = 25 cr
& frac{{x imes 15}}{{100}} = frac{{200 imes 15}}{{100}} = 30 cr
& { ext{Less}}\% = frac{5}{{30}} imes 100 = 16frac{2}{3}\% cr} $$
[#119] The ratio of expenditure to savings of a woman is 5 : 1. If her income and expenditure are increased by 10% and 20%, respectively, then find the percentage change in her savings.
Correct Answer
(D) 40%
Explanation
Solution: [x08egin{array}{*{20}{c}}
{{ ext{Income}}}&{{ ext{Expenditure}}}&{{ ext{Saving}}} \
x08egin{gathered}
600 hfill \
,,,,,,,,,,{ downarrow ^{ + 10\% }} hfill \
660 hfill \
end{gathered} &x08egin{gathered}
500 hfill \
,,,,,,,,,{ downarrow ^{ + 20\% }} hfill \
600 hfill \
end{gathered} &x08egin{gathered}
100 hfill \
hfill \
60 hfill \
end{gathered}
end{array}] Decrease in saving = $$frac{{40}}{{100}}$$ × 100 = 40%
[#120] A is 80% more than B and C is $$48frac{4}{7}\% $$ xa0less than the sum of A and B. By what percent is C less than A?
Correct Answer
(D) 20
Explanation
Solution: $$eqalign{
& {x08f{Given:}} cr
& { ext{A is }}80\% { ext{ more than B}} cr
& { ext{C is }}48frac{4}{7}\% { ext{ less than A}} + { ext{B}} cr
& {x08f{Formula}},{x08f{used:}} cr
& 80\% o frac{4}{5} cr
& {x08f{Calculation:}} cr
& Rightarrow { ext{A}} = left( {1 + frac{4}{5}}
ight){ ext{B}} = frac{{9{ ext{B}}}}{5} cr
& Rightarrow { ext{C}} = left( {100\% - 48frac{4}{7}\% }
ight)left( {{ ext{A}} + { ext{B}}}
ight) cr
& Rightarrow { ext{C}} = 51frac{3}{7}\% imes left( {frac{{9B}}{5} + { ext{B}}}
ight) cr
& Rightarrow { ext{C}} = frac{{3.6}}{7} imes frac{{14{ ext{B}}}}{5} cr
& Rightarrow { ext{C}} = frac{{7.2{ ext{B}}}}{5} cr
& { ext{Difference between A and C}} = frac{{1.8{ ext{B}}}}{5} cr
& Rightarrow { ext{Percentage}} = frac{{frac{{1.8{ ext{B}}}}{5}}}{{frac{{9{ ext{B}}}}{5}}} imes 100 cr
& = 0.2 imes 100 cr
& = 20\% cr
& herefore { ext{The required percentage}} = 20\% cr
& cr
& {x08f{Alternate}},{x08f{solution:}} cr
& { ext{Let the value of B be 100}} cr
& Rightarrow { ext{A}} = 100 imes 180\% = 180 cr
& Rightarrow left( {{ ext{A}} + { ext{B}}}
ight) = 280 cr
& { ext{According to the question}} cr
& { ext{C}} = 51frac{3}{7}\% { ext{ of }}280 cr
& Rightarrow { ext{C}} = frac{{360}}{{700}} imes 280 = 144 cr
& { ext{So, required }}\% = frac{{180 - 144}}{{180}} imes 100\% = 20\% cr
& herefore { ext{The required }}\% { ext{ is }}20\% cr} $$