Percentage - Study Mode

[#121] Rohit's income is Rs. 32000. If his expenses is 30 percent of total income, then what will be the saving of Rohit?
Correct Answer

(B) Rs. 22400

Explanation

Solution: Rohit income = 32000 Cost = 30% Saving = 70% Saving = 32000 × $$frac{{70}}{{100}}$$ = 22400

[#122] The price of petrol shot up by 5%. Before the hike, the price was Rs. 82 per litre. A man travels 3045 km every month and his car gives a mileage of 15 km per litre. What is the increase in the monthly expenditure (to the nearest Rs.) on the man's travel due to the hike in the petrol prices?
Correct Answer

(A) 832

Explanation

Solution: Before hike price → Rs. 82 per litre 5% → $$frac{{82 imes 5}}{{100}}$$ xa0= Rs. 4.1 per litre Distance = 3045 km Petrol use = $$frac{{3045}}{{15}}$$ xa0= 203 Increase expenditure = 203 × 4.1 = 832.3 = Rs. 832

[#123] If each edge of a cube is increased by 10% then the percentage increase in its surface area is:
Correct Answer

(A) 21%

Explanation

Solution: $${l_1} o {l_2}$$ [10xrightarrow[{ + 10 uparrow }]{}{l_2}] $$eqalign{
& {S_1} o {S_2} cr
& 6 imes {10^2} o 6 imes {11^2} cr
& 100 o 121 cr
& = frac{{21}}{{100}} imes 100 cr
& = 21\% cr} $$

[#124] If the numerator of a fraction is increased by 15% and denominator is decreased by 20%, then the fraction, so obtained, is $$frac{{17}}{{65}}.$$ xa0What is the original fraction?
Correct Answer

(D) $$frac{{272}}{{1495}}$$

Explanation

Solution: $$eqalign{
& { ext{Let fraction}} = frac{x}{y} cr
& frac{{xleft( {115}
ight)}}{{y imes 80}} = frac{{17}}{{65}} cr
& frac{x}{y} = frac{{17}}{{65}} imes frac{{16}}{{23}} = frac{{272}}{{1495}} cr} $$

[#125] In a two-candidate election, 10% of the voters did not cast their ballots. 10% of the votes cast were found invalid. The winning candidate received 54% of the valid votes and a 1620-vote majority. Find the number of people on the voter list who have registered to vote.
Correct Answer

(A) 25000

Explanation

Solution: Given 10% of the voters did not cast their vote and 10% of the polled vote were found invalid The winner candidate got 54% of the valid vote and beat the opposition by 1620 votes Concept used: The percentage is calculated as based on 100 i.e. 100 is the base 40% means 40 out of 100 Calculation: Let, total enrolled voter be $$x$$ 10% did not cast vote means casted or polled vote = $$frac{{9x}}{{10}}$$ 10% vote is invalid That means valid vote = $$frac{{90}}{{100}} imes frac{{9x}}{{10}}$$ $$ Rightarrow frac{{81x}}{{100}}$$ The winner candidate got 54% of the polled vote means loosed got (100 - 54) = 46% vote Winner candidate got total $$left( {frac{{54}}{{100}} imes frac{{81x}}{{100}}}
ight)$$ xa0 vote And the looser candidate got $$left( {frac{{46}}{{100}} imes frac{{81x}}{{100}}}
ight)$$ xa0 vote Accordingly, $$eqalign{
& left( {frac{{54}}{{100}} imes frac{{81x}}{{100}}}
ight) - left( {frac{{46}}{{100}} imes frac{{81x}}{{100}}}
ight) = 1620 cr
& Rightarrow left( {frac{{81x}}{{100}}}
ight) imes left( {frac{{54 - 46}}{{100}}}
ight) = 1620 cr
& Rightarrow frac{{left( {81 imes 8}
ight)x}}{{10000}} = 1620 cr
& Rightarrow x = frac{{1620 imes 10000}}{{81 imes 8}} cr
& Rightarrow x = 25000 cr} $$ ∴ Total 25000 voters registered in the voter list.