Percentage - Study Mode

[#206] If X is 20% less then Y, then find the value of $$frac{Y - X}{Y}$$xa0 and $$frac{X}{X - Y}$$ :
Correct Answer

(A) $$frac{1}{5}$$, - 4

Explanation

Solution: 20% = $$frac{1}{5}$$ = $$frac{4}{5}$$ Xxa0 : xa0 Y 4 xa0 : xa0 5 Let X = 4a Y = 5a Hence, ⇔ $$frac{Y - X}{Y}$$ = $$frac{5a - 4a}{5a}$$ = $$frac{a}{5a}$$ = $$frac{1}{5}$$ ⇔ $$frac{X}{X - Y}$$ = $$frac{4a}{4a - 5a}$$ = $$frac{4a}{- a}$$ = - 4 Hence required answer = $$frac{1}{5}$$, - 4

[#207] The ratio of the number of boys to that of girls in a school is 4 : 1. If 75% of boys and 70% of the girls are scholarship holders, then the percentage of students who do not get scholarship is :
Correct Answer

(D) 26%

Explanation

Solution: Let the number of boys = 400 Let the number of girls = 100 Total number of students who do not get scholarship = 400 × $$frac{25}{100}$$ + 100 × $$frac{30}{100}$$ = 100 + 30 = 130 Required percentage = $$frac{130}{500}$$ × 100 = 26%

[#208] A man had a certain amount with him. He spent 20% of that to buy any article and 5% of the remaining on transport. Then he gifted Rs. 120. If he is left with Rs. 1400, the amount he spent on transport is :
Correct Answer

(D) Rs. 80

Explanation

Solution: Let the total amount = x According to the question, x × $$frac{80}{100}$$ × $$frac{95}{100}$$ = (120 + 1400) x × $$frac{4}{5}$$ × $$frac{19}{20}$$ = 1520 x = $$frac{1520 × 100}{76}$$ x = 2000 Total amount = 2000 Amount spent on transport = 2000 × $$frac{80}{100}$$ × $$frac{5}{100}$$ = Rs. 80

[#209] The income of a company increases 20% per annum. If its income is Rs. 2664000 in the year 2012. Then its income in the year 2010 was :
Correct Answer

(B) Rs. 1850000

Explanation

Solution: Let the income in 2010 be P ⇒ R = 20% ⇒ Income of year 2012 ⇒ Rs. 2664000 $$eqalign{
& Rightarrow { ext{Income of 2012}} = P{left[ {1 + frac{R}{{100}}}
ight]^2} cr
& Rightarrow 2664000 = P{left[ {1 + frac{{20}}{{100}}}
ight]^2} cr
& Rightarrow 2664000 = P imes frac{6}{5} imes frac{6}{5} cr
& Rightarrow { ext{Income in 2010 = 1850000}} cr} $$

[#210] An individual pays 30% income tax. On this he has to pay a surcharge of 10%. Thus, the net tax rate, he has pay is :
Correct Answer

(C) 33%

Explanation

Solution: Net tax rate = 30 + $$frac{30 × 10}{100}$$ = 33%