Percentage - Study Mode

[#221] A student multiplied a number with $$frac{3}{4}$$ instead of $$frac{4}{3}.$$ What is the error percentage?
Correct Answer

(B) 43.75%

Explanation

Solution: $$eqalign{
& frac{3}{4},,frac{4}{3} cr
& { ext{LCM of 4, 3}} = 12 cr
& { ext{First number}} cr
& = frac{3}{4} imes 12 = 9 cr
& { ext{Second number}} cr
& = frac{4}{3} imes 12 = 16 cr
& { ext{Error percentage}} cr
& = frac{7}{{16}} imes 100 = 43frac{3}{4}\% = 43.75\% cr} $$

[#222] A person saves $$33frac{1}{3}\% $$ xa0of his income. If the saving increases by 22% and the expenditure increases by 10%, then the percentage increase in his income is:
Correct Answer

(A) 14%

Explanation

Solution: $$eqalign{
& 33frac{1}{3}\% = frac{1}{3} cr
& { ext{Let income}} = 300 cr
& { ext{Saving}} = 100 cr
& { ext{Expenditure}} = 300 - 100 = 200 cr} $$ [x08egin{array}{*{20}{c}}
{}&{{ ext{Income}}}& = &{{ ext{Expenditure}}}& + &{{ ext{Saving}}} \
{{ ext{Old}} o }&{300}& = &{200}& + &{100} \
{}&{}&{}&{,,,,,,,,,,{ downarrow ^{ + 10\% }}}&{}&{,,,,,,,,,,{ downarrow ^{ + 22\% }}} \
{{ ext{New}} o }&x& = &{220}& + &{122}
end{array}] $$eqalign{
& x = 220 + 122 = 342 cr
& { ext{Increase}} = 342 - 300 = 42 cr
& { ext{Increase }}\% = frac{{42}}{{300}} imes 100 = 14\% cr} $$

[#223] The sum of weights of A and B is 80 kg. 50% of A's weight is $$frac{5}{6}$$ times the weight of B. Find the difference between their weights.
Correct Answer

(A) 20 kg

Explanation

Solution: $$eqalign{
& { ext{A}} + { ext{B}} = 80 cr
& { ext{A}} imes frac{1}{2} = frac{5}{6}{ ext{B}} cr
& frac{{ ext{A}}}{{ ext{B}}} = frac{5}{3} cr} $$ $$eqalign{
& 8,{ ext{unit}} o 80{ ext{ kg}} cr
& 1,{ ext{unit}} o 10{ ext{ kg}} cr
& 2,{ ext{unit}} o x08oxed{20{ ext{ kg}}} cr} $$

[#224] In an election, candidate X got 70% of the overall valid votes. If 20% of the overall votes were declared invalid and the total numbers of votes is 64000, then find the number of valid votes polled in favour of the candidate.
Correct Answer

(A) 35840

Explanation

Solution: Total vote = 100 Valid vote = 100 - 20 = 80 X = 70% of 80 = 56 100 unit → 64000 1 unit → 640 56 unit → 56 × 640 = 35840

[#225] In an election between two candidates, 65% of the voters cast their votes, out of which 3% of the votes were decided to be invalid. A candidate got 81965 votes which are 65% of the total valid votes. What is the total number of votes enrolled in that election?
Correct Answer

(A) 200000

Explanation

Solution: $$eqalign{
& { ext{Valid}} cr
& 65\% o 81965 cr
& 1\% o 1261 cr
& 100\% o 126100 cr
& 65\% { ext{ of }}97\% o 126100 cr
& 65 imes frac{{97}}{{100}} o 126100 cr
& 65mu o 130000 cr
& 100mu o 200000 cr} $$