Percentage - Study Mode
[#391] If decreasing 110 by x% gives the same result as increasing 50 by x%, then x% of 650 is what percentage (correct to the nearest integer) more than (x - 10)% of 780?
Correct Answer
(D) 14%
Explanation
Solution: $$eqalign{
& 110 imes frac{{left( {100 - x}
ight)}}{{100}} = 50 imes frac{{left( {100 + x}
ight)}}{{100}} cr
& 11left( {100 - x}
ight) = 5left( {100 + x}
ight) cr
& 1100 - 11x = 500 + 5x cr
& 16x = 600 cr
& x = frac{{800}}{{16}} = frac{{75}}{2} = 37frac{1}{2}\% cr
& { ext{Now,}} cr
& { ext{650}} imes frac{{75}}{{200}} o 780 imes frac{{55}}{{200}} cr
& frac{{25}}{2} o 11 cr
& 25 o 22 cr
& = frac{3}{{22}} imes 100 = 14\% cr} $$
[#392] If 25% of 400 + 35% of 1260 + 27% of 1800 = 1020 + x, then the value of x lies between:
Correct Answer
(A) 6 to 10
Explanation
Solution: 400 × 25% + 1260 × 35% + 180 × 27% = 1020 + x 100 + 441 + 486 = 1020 + x 1027 = 1020 + x x = 7
[#393] The monthly salary of a person was Rs. 50,000. He used to spend on family expenses (E), Taxes (T), Charity (C), and the rest were his saving. E was 60% of the income, T was 20% of E, and C was 15% of T. When his salary got raised by 40%, he maintained the percentage level of E, but T becomes 30% of E and C becomes 20% of T. The difference between the two savings (in Rs.) is:
Correct Answer
(B) 220
Explanation
Solution: Income = Rs. 50,000 [x08egin{array}{*{20}{c}}
{{ ext{Income}}}& = &{50,000}&{70,000} \
{}&{}&{,,,,,, downarrow 60\% }&{,,,,,, downarrow 60\% } \
{{ ext{Expenses}}}& = &{30,000}&{42,000} \
{}&{}&{,,,,,, downarrow 20\% }&{,,,,,, downarrow 30\% } \
{{ ext{Tax}}}& = &{6,000}&{12,600} \
{}&{}&{,,,,,, downarrow 15\% }&{,,,,,, downarrow 20\% } \
{{ ext{Charity}}}& = &{900}&{2,520} \
{{ ext{Saving}}}& = &{overline {underline {,,13,100,,} } }&{overline {underline {,,12,880,,} } }
end{array}] Difference the savings = Rs. 13,100 - Rs. 12,880
= Rs. 220
[#394] Raju spends 10 percent and 20 percent of his income on transport and food respectively. He spends 30 percent of the remaining income on clothing. He saves rest of his income. If his saving is Rs. 26460, then what will be total expenditure on food and clothing together?
Correct Answer
(B) Rs. 22140
Explanation
Solution: $$eqalign{
& { ext{Let, total income is }}100 cr
& { ext{Transport costs}} = 100 imes frac{{10}}{{100}} = 10 cr
& { ext{Food costs}} = 100 imes frac{{20}}{{100}} = 20 cr
& { ext{Remain}} = 100 - left( {20 + 10}
ight) = 70 cr
& { ext{Clothes costs}} = 70 imes frac{{30}}{{100}} = 21 cr
& { ext{Saving}} = 100 - left( {10 + 20 + 21}
ight) = 49 cr
& { ext{Cost on food and clothes}} = 20 + 21 = 41 cr
& 49 o 26460 cr
& 1 o 540 cr
& herefore 41 o 540 imes 41 = { ext{Rs}}{ ext{. }}22,140 cr} $$
[#395] The monthly salaries of A and B are the same. A, B and C donate 10%, 8% and 9% respectively, of their monthly salaries to a charitable trust. The difference between the donations of A and B is Rs. 400. The total donation by A and B is Rs. 900 more than that of C. What is the monthly salary of C?
Correct Answer
(B) Rs. 30,000
Explanation
Solution: Let the salary of A and B be 100x each and C be 100y Money donate by A = 100x × $$frac{{10}}{{100}}$$ = 10x Money donate by B = 100x × $$frac{8}{{100}}$$ = 8x Money donate by C = 100y × $$frac{9}{{100}}$$ = 9y According to the question ⇒ 10x - 8x = 400 ⇒ 2x = 400 ⇒ x = 200 Total donation of A and B = 10x + 8x = 18x ⇒ 18 × 200 = 3600 The total donation by A and B is Rs. 900 more than that of C ⇒ 3600 - 9y = 900 ⇒ 9y = 2700 ⇒ y = 300 Monthly salary of C = 100y = 100 × 300 = 30000 ∴ Monthly salary of C is Rs. 30000