Percentage - Study Mode

[#256] The ratio 5 : 4 expressed as a percent equals :
Correct Answer

(D) 125%
(E) 125%

Explanation

Solution: 5 : 4 = $$frac{5}{4}$$ = $$frac{5}{4}$$ × 100% = 125%

[#257] Solve (550% of 250) ÷ 275 = (?)
Correct Answer

(D) None of these

Explanation

Solution: Given (550% of 250) ÷ 275 = (?) ⇒ (?) = $$frac{550 × 250}{100}$$ xa0 ÷ 275 ⇒ (?) = (55 × 25) ÷ 275 ⇒ (?) = $$frac{55 × 25}{275}$$ ⇒ (?) = 5

[#258] 270 candidates appeared for an examination, of which 252 passed. The pass percentage is :
Correct Answer

(D) $$93frac{1}{3}$$%

Explanation

Solution: Pass percentage : $$eqalign{
& = left( {frac{{252}}{{270}} imes 100}
ight)\% cr
& = frac{{280}}{3}\% cr
& = 93frac{1}{3}\% cr} $$

[#259] What will come in the place of (?) in the expression below : x% of y is y% of (?)
Correct Answer

(A) x

Explanation

Solution: x% of y = $$frac{xy}{100}$$..... (i) And y% of x = $$frac{xy}{100}$$ ..... (ii) From (i) and (ii) x% of y = y% of x

[#260] In the expression xy 2 , the value of both variables x and y are decreased by 20%. By this, the value of the expression is decreased by :
Correct Answer

(B) 48.8%

Explanation

Solution: Let X and Y denote the new values of x and y respectively. Then, X = 80% of x = $$frac{4x}{5}$$ Y = 80% of y = $$frac{4y}{5}$$ $$eqalign{
& herefore X{Y^2} = frac{{4x}}{5} imes {left( {frac{{4y}}{5}}
ight)^2} cr
& ,,,,,,,,,,,,,,,,,, = frac{{4x}}{5} imes frac{{16{y^2}}}{5} cr
& ,,,,,,,,,,,,,,,,,, = frac{{64}}{{125}}x{y^2} cr} $$ Decrease in the value : $$eqalign{
& = left( {x{y^2} - frac{{64}}{{125}}x{y^2}}
ight) cr
& = frac{{61}}{{125}}x{y^2} cr} $$ ∴ Decrease % $$eqalign{
& = frac{{61}}{{125}}x{y^2} cr
& = left( {frac{{61x{y^2}}}{{125}} imes frac{1}{{x{y^2}}} imes 100}
ight)\% cr
& = 48.8\% cr} $$