Percentage - Study Mode

[#496] Reena goes to a shop to buy a radio costing Rs. 2568. The rate of sales tax is 7% and the final value is rounded off to the next higher integer. She tells the shopkeeper to reduce the price of the radio so that she has to pay Rs. 2568 inclusive of sales tax. Find the reduction needed in the price of the radio.
Correct Answer

(C) Rs. 168

Explanation

Solution: $$eqalign{
& { ext{Reduction}} cr
& = {frac{7}{{107}}} imes 2568 cr
& = 168 cr} $$

[#497] Australia scored a total of X runs in 50 overs. India tied the scores in 20% less overs. If India's average run rate had been 33.33% higher the scores would have been tied 10 overs earlier. Find how many runs were scored by Australia?
Correct Answer

250

Explanation

Solution: Since, Run scored = Over × Run rate If overs is reduced by 25%, run rate will go up by 33.33%. Hence, Australia could have scored any number of runs.

[#498] In 2000, the market shares of the toilet soaps Margo, Palmolive and dove were 40%, 30% and 30% respectively. Starting from the next year, a new soap enters into the market each year and gets 10% of the market share. The existing soap share the remaining market share in the same ratio as they did in the previous year. What percent of the total market share will mango have in 2002?
Correct Answer

(C) 32.4%

Explanation

Solution: In 2000, the market share was 40%, 30% and 30%, means the ratio is 4 : 3 : 3 In 2001, a new product (A) enters and has 10% market share, 90% of the remaining market is shared by the previous 3. Now, divide 90% in the ratio 4 : 3 : 3 , i.e 36%, 27%, 27%. Now the ratio is 36 : 27 : 27 : 10 In 2002, another new product (B) enters and has 10% market share, now the remaining 90% market share is distributed in the ratio, 36 : 27 : 27 : 10 and hence remaining 32.4%, 24.3%, 24.3%, 9% Thus, the market share of Margo in 2002 is 32.4%

[#499] In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?
Correct Answer

(A) 30000

Explanation

Solution: $$eqalign{
& { ext{Let the total number of applicants be x}}. cr
& { ext{Number of eligible candidates}} cr
& = { ext{ }}95\% { ext{ }}of{ ext{ }}x cr
& { ext{Eligible candidates of other categories}}, cr
& = 15\% ,of,left( {95\% { ext{ }}of{ ext{ }}x}
ight) cr
& = {frac{{15}}{{100}}} imes {frac{{95}}{{100}}} imes x cr
& = frac{{57}}{{400}}x cr
& or,left( {frac{{57}}{{400}}}
ight)x cr
& x = frac{{ {4275 imes 400} }}{{57}} cr
& ,,,,,, = 30000 cr} $$

[#500] In an election between two candidates, 85% of the voters cast their votes, out which 4% of the votes were declared invalid. A candidate got 6936 votes which were 85% of the valid votes. Find the total number of voters enrolled in that election.
Correct Answer

(D) 10,000

Explanation

Solution: $$eqalign{
& 72.25mu o 6936 cr
& 100mu o frac{{6936 imes 100}}{{72.25}} cr
& 100mu o 9600 cr
& Rightarrow { ext{Valid votes }}96mu o 9600 cr
& 1mu o 100 cr
& 100mu o 10000{ ext{ Answer}} cr} $$