Percentage - Study Mode

[#186] If radius of a circle is increased by 5%, then the increase in it's area is :
Correct Answer

(A) 10.25%

Explanation

Solution: Quicker approach $$ uparrow $$ xa0 in A = a + b + $$frac{ab}{100}$$ Here a = b = 5% $$ uparrow $$ xa0 in A : $$eqalign{
& = left( {5 + 5 + frac{{5 imes 5}}{{100}}}
ight)\% cr
& = 10.25\% cr} $$

[#187] If 60% of A's income is equal to 75% of B's income, then B's income is equal to x% of A's income. The value of x is :
Correct Answer

(C) 80

Explanation

Solution: According to the question, ⇒ 60 × $$frac{A}{100}$$ = 75 × $$frac{B}{100}$$ ⇒ 4A = 5B ⇒ B = $$frac{4}{5}$$A ⇒ A × $$frac{x}{100}$$ = B (given) ⇒ A × $$frac{x}{100}$$ = $$frac{4}{5}$$A ⇒ x = 80

[#188] A dozen pairs of socks quoted at Rs. 180 are available at discount of 20%. How many pairs of socks can be bought for Rs. 48 ?
Correct Answer

(B) 4 pairs

Explanation

Solution: Price after discount = $$frac{180 × 80}{100}$$ = Rs. 144 Price of 1 pair of socks = Rs. $$frac{144}{12}$$ = Rs. 12 Required number of pairs = $$frac{48}{12}$$ = 4 pairs

[#189] If the population of a town is 64000 and its annual increase is 10%, then its population at the end of 3 years will be :
Correct Answer

(B) 85184

Explanation

Solution: Present population = 64000 1 st year = 66400 2 nd year = 6400 + 640 3 rd year = 6400 + 2 × 640 + 64 Total population after 3 years = 64000 + 3 × 6400 + 3 × 640 + 64 = 85184 Alternate: Population after n years $$eqalign{
& Rightarrow { ext{p}}' = { ext{p}}{left( {1 pm frac{{ ext{R}}}{{100}}}
ight)^{ pm { ext{n}}}} cr
& { ext{p}}' = 64000{left( {1 pm frac{{10}}{{100}}}
ight)^3} cr
& ,,,,,,,, = 85184 cr} $$

[#190] In a village three people contested for the post of village Pradhan. Due to their own interest, all the voters voted and no one vote was invalid. The losing candidate got 30% votes. What could be the minimum absolute margin of votes by which the winning candidate led by the nearest rival, if each candidate got an integral percent of votes ?
Correct Answer

(B) 2

Explanation

Solution: Let total votes in village = 100 Losing candidate got votes = 30% of 100 = 30 votes Winner's and nearer rival's votes = 100 - $$frac{13}{100}$$ × 100 = 70 ∴ If both get equal votes then, it should be, 35 ∴ Minimum difference between winner and nearer rival = (36 - 34) = 2