Percentage - Study Mode

[#111] In an examination, 34% of the students failed in Mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then the percentage of students who passed in both the subjects was :
Correct Answer

(D) 56%

Explanation

Solution: $$eqalign{
& nleft( A
ight) = 34 cr
& nleft( B
ight) = 42 cr
& nleft( {A cap B}
ight) = 20 cr
& { ext{So, }} cr
& { ext{n}}left( {A cup B}
ight) cr
& = nleft( A
ight) + nleft( B
ight) - nleft( {A cap B}
ight) cr
& = 34 + 42 - 20 cr
& = 56 cr} $$ ∴ Percentage failed in either or both the subjects = 56%

[#112] If x% of a is the same as y% of b, then z% of b is :
Correct Answer

(C) $$frac{{xz}}{y}\% { ext{ of }}a$$

Explanation

Solution: $$eqalign{
& x\% { ext{ of }}a = y\% { ext{ of }}a cr
& Rightarrow frac{x}{{100}}a = frac{y}{{100}}b cr
& Rightarrow b = left( {frac{x}{y}}
ight)a cr
& herefore z\% { ext{ of }}b: cr
& = left( {z\% { ext{ of }}frac{x}{y}}
ight)a cr
& = left( {frac{{xz}}{{y imes 100}}}
ight)a cr
& = left( {frac{{xz}}{y}}
ight)\% { ext{ of }}a cr} $$

[#113] In the price of sugar falls by $$2frac{1}{2}\% $$ , a person can buy 9 kg more of sugar for Rs. 1260 than before. If the price had risen by $$12frac{1}{2}\% $$ , how much sugar would he have bought for the same sum ?
Correct Answer

(B) 312 kg

Explanation

Solution: Let the original price of sugar be Rs. $$x$$ per kg Then, reduced price : $$eqalign{
& 97frac{1}{2}\% { ext{ of Rs}}{ ext{. }}x cr
& = { ext{Rs}}{ ext{. }}left( {frac{{195}}{2} imes frac{1}{{100}} imes x}
ight) cr
& = { ext{Rs}}{ ext{. }}frac{{39x}}{{40}} cr
& herefore frac{{1260}}{{left( {frac{{39x}}{{40}}}
ight)}} - frac{{1260}}{x} = 9 cr
& Rightarrow frac{{16800}}{{13x}} - frac{{1260}}{x} = 9 cr
& Rightarrow 13x = frac{{420}}{9} cr
& Rightarrow x = frac{{140}}{{39}} cr} $$ Increased price : $$eqalign{
& 112frac{1}{2}\% { ext{ of Rs}}{ ext{. }}frac{{140}}{{39}} cr
& = { ext{Rs}}{ ext{. }}left( {frac{{225}}{2} imes frac{1}{{100}} imes frac{{140}}{{39}}}
ight) cr
& = { ext{Rs}}{ ext{. }}frac{{105}}{{26}} cr} $$ ∴ Quiantity of sugar bought for Rs. 1260 : $$eqalign{
& = left( {1260 imes frac{{26}}{{105}}}
ight){ ext{ kg}} cr
& = { ext{312 kg}} cr} $$

[#114] At a special sale, 5 tickets can be purchased for the price of 3 tickets. If 5 tickets are purchased at the sale, the amount saved will be what percent of the original price of the 5 tickets ?
Correct Answer

(C) 40%

Explanation

Solution: Let the original price of each ticket be Rs. 100 Then, original price of 5 tickets = Rs. 500 Sale price of 5 tickets = Rs. 300 Amount saved : = Rs. (500 - 300) = Rs. 200 ∴ Required percentage : = $$left( {frac{{200}}{{500}} imes 100}
ight)$$ xa0% = 40%

[#115] The price of sugar per kg increased from Rs. 16 to Rs. 20. The percentage reduction in the use of sugar so that the expenditure does not increase, should be :
Correct Answer

(B) 20%

Explanation

Solution: Let original consumption = 100 kg and new consumption = $$x$$ kg So, ⇔ 100 × 16 = $$x$$ × 20 ⇔ $$x$$ = 80 ∴ Reduction in consumption = 20%