Percentage - Study Mode

[#176] If 25% of half of x is equal to 2.5 times the value of 30% of one fourth of y, then x is what percent more or less than y?
Correct Answer

(A) 50% more

Explanation

Solution: $$eqalign{
& y imes frac{1}{4} imes frac{{30}}{{100}} imes 2.5 = x imes frac{1}{4} imes frac{1}{2} cr
& frac{x}{y} = frac{3}{2} cr
& x:y = underbrace {3,:,2}_{ + 1} cr
& \% = frac{1}{2} imes 100 = 50\% cr} $$

[#177] A fruit seller sells 45% of the oranges that he has along with one more orange to a customer. He then sells 20% of the remaining oranges and 2 more oranges to a second customer. He then sells 90% of the now remaining oranges to a third customer and is still left with 5 oranges. How many oranges did the fruit seller have initially?
Correct Answer

(D) 120

Explanation

Solution: $$eqalign{
& { ext{Let total numbe of oranges}} = x cr
& left{ {left( {frac{{x imes 55}}{{100}} - 1}
ight) imes frac{{80}}{{100}} - 2}
ight} imes frac{{10}}{{100}} = 5 cr
& left( {frac{{x imes 55}}{{100}} - 1}
ight) imes frac{{80}}{{100}} = 50 + 2 cr
& left( {frac{{x imes 55}}{{100}} - 1}
ight) = frac{{52 imes 10}}{8} cr
& frac{{x imes 55}}{{100}} - 1 = 65 cr
& frac{{x imes 55}}{{100}} = 66 cr
& x = frac{{66 imes 100}}{{55}} cr
& x = 120 cr} $$

[#178] A's salary is 50% more than that of B. Then B's salary is less than that of A by :
Correct Answer

(B) $$33frac{1}{3}$$%

Explanation

Solution: Let salary of B = 100 ∴ Salary of A = 100 + 50% of 100 = 150 B salary is lesser then A = 150 - 100 = 50 Required % = $$frac{50}{150}$$ × 100 = $$33frac{1}{3}$$%

[#179] If 60% of A = 30% of B, B = 40% of C and C = x% of A, then value of x is :
Correct Answer

(D) 500%

Explanation

Solution: According to the question, A : B : C 1 : 2 : 5 ( 60A = 30B) $$frac{A}{B}$$ = $$frac{1}{2}$$ C = 5 A = 1 Required answer = $$frac{5}{1}$$ × 100 = 500%

[#180] In an examination 70% of the candidate passed in English, 80% passed in Mathematics, 10% failed in both subjects. If 144 candidates passed in both, the total number of candidates was :
Correct Answer

(C) 240

Explanation

Solution: Failed candidates in English = (100 - 70) = 30% Failed candidates in Mathematics = (100 - 80) = 20% Candidates who fail in both subject = 10%
Candidates who only fail in English = 30 - 10 = 20% Candidates who only fail in Mathematics = 20 - 10 = 10% Percentage of passed students in both subject = 100 - (Candidates who only fail in English + Candidates who only fail in Mathematics + Candidates who fail in both subject) = 100 - (20 + 10 + 10) = 60% According to the question, 60% of students = 144 Total students : = $$frac{144}{60}$$ × 100 = 240