Percentage - Study Mode

[#416] The population of village is 1,00,000. The rate of increase is 10% per annum. Find the population at the start of the third year?
Correct Answer

(B) 1,21,000

Explanation

Solution: 100000 == 10%↑(1 st year) ==> 110000 == 10%↑(2 nd year) ==> 121000 Population at starting of 3 rd year = 121000 [By using net percentage change method, we have saved our self from cumber some formulas on population which is based on compound interest].

[#417] In the recent, climate conference in New York, out of 700 men, 500 women, 800 children present inside the building premises, 20% of the men, 40% of the women and 10% of the children were Indians. Find the percentage of people who were not Indian?
Correct Answer

(C) 79%

Explanation

Solution: Number of Indians men present there = $$frac{{700 imes 20}}{{100}} = 140$$ Indian women = $$frac{{500 imes 40}}{{100}} = 200$$
Indian children = $$frac{{800 imes 10}}{{100}} = 80$$ Total member present in climate conference = 700 + 500 + 800 = 2000 Total Indian = 200 + 140 + 80 = 420 Hence, % of Indian present there = $$frac{{420 imes 100}}{{2000}} = 21\% $$ % of people who were not Indian = 100 - 21 = 79%

[#418] Out of the total production of iron from hematite, an ore of Iron, 20% of the ore gets wasted, and out of the remaining iron, only 25% is pure iron. If the pure iron obtained in a year from a mine of hematite was 80,000 kg, then the quantity of hematite mined from that mine in the year is
Correct Answer

(B) 4,00,000 kg

Explanation

Solution: Let 100 kg of hematite be obtained then 20% of it get wasted that means 80 kg of ore remains. Pure iron = 25% of remaining ore = $$frac{{80 imes 25}}{{100}} = 20,{ ext{kg}}$$ 20 kg pure Iron is obtained from 100 of hematite 1 kg pure Iron is obtained from = $$frac{{100}}{{20}}$$ hematite Then, 80000 kg pure Iron is obtained from =$$,frac{{100}}{{20}} imes 80000 = ,$$ xa0 xa0$$400000,{ ext{kg}}$$ xa0 hematite.

[#419] A man buys a truck for Rs. 2,50,000. The annual repair cost comes to 2% of the price of purchase. Besides, he has to pay an annual tax of Rs. 2000. At what monthly rent must he rent out the truck to get a return of 15% on his net invests of the first year?
Correct Answer

(D) Rs. 3212.5

Explanation

Solution: The total cost for the year = 250000 + 2% of 2500000 + 2000 = Rs. 257000
For getting return of 15% he must earn = $$frac{{257000 imes 15}}{{100}}$$ = Rs. 38550 per year
Then, Monthly Rent = $$frac{{38550}}{{12}}$$ = Rs. 3212.5

[#420] Ram spends 30% of his salary on house rent, 30% of the rest he spends on his children's education and 24% of the total salary he spends on clothes. After his expenditure, he is left with Rs. 2500. What is Ram's salary?
Correct Answer

(C) Rs. 10,000

Explanation

Solution: Let Ram's salary be x
He spends on rent = 30% of x = $$frac{{30{ ext{x}}}}{{100}}$$
He spends on education = 30% from rest of the salary = $$frac{{30 imes 70{ ext{x}}}}{{100 imes 100}} = frac{{21{ ext{x}}}}{{100}}$$
He Spends on clothes = 24% of total salary = $$frac{{24{ ext{x}}}}{{100}}$$
Saving = 2500 Salary of ram = x $$eqalign{
& frac{{30{ ext{x}}}}{{100}} + frac{{21{ ext{x}}}}{{100}} + frac{{24{ ext{x}}}}{{100}} + 2500 = { ext{x}} cr
& { ext{or,}},frac{{75x}}{{100}} = { ext{x}} - 2500 cr
& { ext{or,}},75{ ext{x}} = 100{ ext{x}} - 250000 cr
& { ext{or, }}100{ ext{x}} - 75{ ext{x}} = 250000 cr
& { ext{or, x}} = frac{{250000}}{{25}} cr
& { ext{or, x}} = 10000 cr
& { ext{Ram's}},{ ext{salary = Rs}}{ ext{.}},10000 cr} $$