Percentage - Study Mode

[#231] Two successive price increases of 10% each on an article are equivalent to a single price increase of :
Correct Answer

(C) 21%

Explanation

Solution: Let the original price be Rs. $$x$$ New final price : = 110% of (110% of Rs. 100) = Rs. $$left( {frac{{110}}{{100}} imes frac{{110}}{{100}} imes 100}
ight)$$ = Rs. 121 ∴ Total increase : = (121 - 100)% = 21%

[#232] In a market research project, 20% opted for Nirma detergent whereas 60% opted for Surf Blue detergent. The remaining individuals were not certain. If the difference between those who opted for Surf Blue and those who were uncertain was 720, how many respondents were covered in the survey ?
Correct Answer

(B) 1800

Explanation

Solution: Let the total number of respondents be $$x$$ Percentage of uncertain individuals : = [100 - (20 + 60)]% = 20% ∴ 60% of $$x$$ - 20% of $$x$$ = 720 ⇒ 40% of $$x$$ = 720 ⇒ $$frac{{40x}}{{100}}$$ = 720 ⇒ $$x$$ = $$left( {frac{{720 imes 100}}{{40}}}
ight)$$ ⇒ $$x$$ = 1800

[#233] In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examinations ?
Correct Answer

(A) 30000

Explanation

Solution: Let the total number of applicants be $$x$$ Number of eligible candidates = 95 % of $$x$$ Eligible candidates of other categories = 15% of (95 of $$x$$) = $$left( {frac{{15}}{{100}} imes frac{{95}}{{100}} imes x}
ight)$$ = $$frac{{57x}}{{400}}$$ ∴ $$frac{{57x}}{{400}}$$ = 4275 ⇒ $$x$$ = $$left( {frac{{4275 imes 400}}{{57}}}
ight)$$ ⇒ $$x$$ = 30000

[#234] the price of sugar increases by 32%. A family reduces its consumption so that the expenditure of the sugar is up only by 10%. If the total consumption of the sugar before the price rise was 10 kg per month, then the consumption of sugar per month at present (in kg) is :
Correct Answer

(A) $$8frac{1}{3}$$

Explanation

Solution: Let the original price of sugar be Rs. 10 per kg Then, original expenditure = Rs. (10 × 10) = Rs. 100 New expenditure = 110% of Rs. 100 = Rs. 110 New price of sugar = 132% of Rs. 10 = Rs. 13.20 New consumption : = $$frac{110}{13.20}$$ kg = $$frac{25}{3}$$ kg = $$8frac{1}{3}$$ kg

[#235] On a test consisting of 250 questions, Jassi answered 40% of the first 125 questions correctly. What percent of the other 125 questions does she need to answer correctly for her grade on the entire exam to be 60% ?
Correct Answer

(C) 80%
(G) 80%

Explanation

Solution: Number of questions answered correctly : = 40% of 125 = 50 For 60% grade, number of questions to be answered correctly : = 60% of 250 = 150 Remaining number of question to be answered correctly : = 150 - 50 = 100 ∴ Required percentage : = $$left( {frac{{100}}{{125}} imes 100}
ight)\% $$ = 80%