Percentage - Study Mode

[#301] A bag contains 600 coins of 25p denomination and 1200 coins of 50p denomination. If 12% of 25p coins and 24% of 50p are removed, the percentage of money removed from the bag is nearly :
Correct Answer

(C) 21.6%

Explanation

Solution: Total money : $$eqalign{
& = { ext{Rs}}{ ext{. }}left( {600 imes frac{{25}}{{100}} + 1200 imes frac{{50}}{{100}}}
ight) cr
& = { ext{Rs}}{ ext{. 750}} cr} $$ 25 paise coins removed : $$eqalign{
& = left( {frac{{12}}{{100}} imes 600}
ight) cr
& = 72 cr} $$ 50 paise coins removed : $$eqalign{
& = left( {frac{{24}}{{100}} imes 1200}
ight) cr
& = 288 cr} $$ Money removed : $$eqalign{
& = { ext{Rs}}{ ext{. }}left( {72 imes frac{{25}}{{100}} + 288 imes frac{{50}}{{100}}}
ight) cr
& = { ext{Rs}}{ ext{. 162}} cr} $$ ∴ Required percentage : $$eqalign{
& = left( {frac{{162}}{{750}} imes 100}
ight)\% cr
& = 21.6\% cr} $$

[#302] Mr. More spent 20% of his monthly income on food and 15% on children's education. 40% of the remaining he spent on entertainment and transport together and 30% on medical. He is left with an amount of Rs. 8775 after all these expenditures. What is Mr. More's monthly income ?
Correct Answer

Rs. 35000

Explanation

Solution: Let Mr. More's monthly income be Rs. $$x$$ Then, [100 - (40 + 30)]% of [100 - 20 + 15]% of $$x$$ = 8775 ⇒ 30% of 65% of $$x$$ = 8775 ⇒ $$left( {frac{{30}}{{100}} imes frac{{65}}{{100}} imes x}
ight)$$ xa0 = 8775 ⇒ $$frac{39}{200}$$ $$x$$ = 8775 ⇒ $$x$$ = $$left( {frac{{8775 imes 200}}{{39}}}
ight)$$ ⇒ $$x$$ = 45000

[#303] If the price of erasers goes down by 25%, a man can buy 2 more erasers for a rupee. How many erasers are available for a rupee ?
Correct Answer

(C) 6

Explanation

Solution: Let the original price of an eraser be Rs. x Reduced price = 75% of Rs. x = Rs. $$frac{3x}{4}$$ $$eqalign{
& herefore frac{1}{{left( {frac{{3x}}{4}}
ight)}} - x = 2 cr
& Rightarrow frac{4}{{3x}} - frac{1}{x} = 2 cr
& Rightarrow frac{1}{{3x}} = 2 cr
& Rightarrow 6x = 1 cr
& Rightarrow x = frac{1}{6} cr} $$ Hence, number of erasers available for a rupee = 6

[#304] Find the : (550% of 250) ÷ 275 = ?
Correct Answer

15

Explanation

Solution: = (550% of 250) ÷ 275 = $$frac{550}{100}$$ × 250 × $$frac{1}{275}$$ = $$frac{55 × 25}{275}$$ = 5

[#305] By how much percent is four-fifths of 70 lesser than five-sevenths of 112 ?
Correct Answer

(B) 30%

Explanation

Solution: $$frac{4}{5}$$ × 70 = 56 and $$frac{5}{7}$$ × 112 = 80 ∴ Required percentage : $$eqalign{
& = left( {frac{{80 - 56}}{{80}} imes 100}
ight)\% cr
& = left( {frac{{24}}{{80}} imes 100}
ight)\% cr
& = 30\% cr} $$