Percentage - Study Mode
[#491] What is the percentage change in the result when we add 50 to a certain number x, instead of subtracting 50 from the same number x?
Correct Answer
50%
Explanation
Solution: If we take different values of x then, Let x = 150, then error% $$eqalign{
& = frac{{ {frac{{ {200 - 100} }}{{100}}} }}{{100}} cr
& = 100\% cr} $$ Again if x = 100, then error% $$eqalign{
& = frac{{ {left( {150 - 50}
ight) imes 100} }}{{100}} cr
& = 200\% cr} $$ If we take different value of x, we get different answer so we can't determine it.
[#492] In a school, there are 100 students. 60% of the students are boys, 40% of whom play hockey and the girls don't play hockey, 75% of girls play badminton. There are only two games to be played. The number of student who don't play any game is:
Correct Answer
10%
Explanation
Solution: Total student = 100
Boys = 60
Girls = 40
Boys who plays hockey = 40% = 24
There is no information about boys who play badminton.
Girls who plays Badminton = 75% = 30
No girls plays hockey. Since, we do not have information that whether the rest of the boys are playing badminton or not. So, we cannot determine the total no. of student who don't play any game.
[#493] A book consist of 30 pages, 25 line on each page and 35 characters on each line. If this content is written in another note book consisting 30 lines and 28 characters per line then the required no. of pages will how much percent greater than previous pages?
Correct Answer
(C) 6.66%
Explanation
Solution: $$eqalign{
& { ext{Let the required number of pages be }}x. cr
& 30 imes 25 imes 35 = x imes 30 imes 28 cr
& x = 31.25 approx 32 cr
& \% ,{ ext{increase}},{ ext{in}},{ ext{number}},{ ext{of}},{ ext{pages}}, cr
& = {frac{2}{{30}}} imes 100 cr
& = 6.66\% cr} $$
[#494] A fraction in reduced form is such that when it is squared and then its numerator is increased by 25% and the denominator is reduced t0 80% it results in $$frac{5}{8}$$ of original fraction. The product of the numerator and denominator is :
Correct Answer
(C) 10
Explanation
Solution: $$eqalign{
& { ext{Let}},{ ext{the}},{ ext{fraction}},{ ext{be}},frac{{100x}}{{100y}} cr
& { ext{Now}},{ ext{according}},{ ext{to}},{ ext{the}},{ ext{question}}, cr
& {left( {frac{{100x}}{{100y}}}
ight)^2} = frac{{125{x^2}}}{{80{y^2}}} = frac{{25{x^2}}}{{16{y^2}}} cr
& frac{{25{x^2}}}{{16{y^2}}} = frac{5}{8}left( {frac{{100x}}{{100y}}}
ight) cr
& {frac{{100x}}{{100y}}} = frac{2}{5} cr
& { ext{hence}}, cr
& { ext{product of numerator and denominator}} cr
& = 2 imes 5 = 10 cr} $$
[#495] 80% of a number added to 80 gives the result as the number itself, then the number is :
Correct Answer
(C) 400
Explanation
Solution: Let X be the number which is added to 80 80% of X = 0.8X Now, 80 + 0.8X = X 0.2X = 80 X = $$frac{{80}}{{0.2}} = 400$$