Percentage Questions with Solutions — Set 21 (Q201 to Q210)

201. The raw material and manufactoring cost formed individually 70% and 30% of the total cost and the profit percentage is 10% of the raw material. If the cost of raw material increases by 20% and that cost of manufacturing is increased by 40% and the selling price is increased by 80%. Then find the new profit percent.

202. In a school 75% students passed in Hindi and 82% students passed in English and 15% failed in both the subjects. If total number of passed candidates is 1872 then find the total number of students and also find failed students in Hindi.

203. Ramesh spends \(12\frac{1}{2}\% \) of his money and then he spends Rs. 1600. After this he spends 20% of the remaining and now left with Rs. 1200. Then find how much money he has initially?

204. Present birth rate per thousand is 45 in a town and the death rate per thousands is 22. Find the net percentage increase in population.

205. Amit gives 1% of his income to his two sons as pocket money every month. The amount received by the sons, 80% goes to elder son and he spends 80% of this amount. If he saves Rs. 40 per month. Find the income of Amit.

206. An amount of 6100 Rs. is distributed among 8 men, 10 women and 12 children in such a way that a man gets 25% more than a woman and each woman gets 25% more than each child. Then find the amount received by each women.

207. In a school number of students increased by 20% this year. But the new law in the country made girls education free all over the country. So to collect the same amount as in the previous year the college management increased the fee of boys by 25%. Then find the ratio of boys in comparison with the girls this year.

208. A house costing Rs. 1464100 was constructed on a piece of land costing Rs. 291600. In what time will the cost of both be same if the cost of land is increasing by 10% annually while the cost of house is decreasing 10% annually?

209. Ankit gives 30% of his total income to his elder daughter and 40% of the remaining to his younger daughter. Then he distributes the remaining money in his three sons equally. If each son gets 812 Rs. then determine how much money did the elder daughter and younger daughter get?

210. A student scores 25% of the total marks and failed by 60 marks. Another student scores 50% of the total marks and thus gets 40 marks more than passing marks. Then by how much  percent the passing marks should be increased to get full marks in the exam?

201. The raw material and manufactoring cost formed individually 70% and 30% of the total cost and the profit percentage is 10% of the raw material. If the cost of raw material increases by 20% and that cost of manufacturing is increased by 40% and the selling price is increased by 80%. Then find the new profit percent.
Sol:-

initial cost = 70 + 30 = 100
initial SP = 100 + 7 = 107
new SP = 107 × \(107 \times \frac{{180}}{{100}}\) = 192.6
new CP = 84 + 42 = 126 ⟹ new % profit = \(\frac{{192.6 – 126}}{{126}} \times 100\) = 5.43%           Answer

202. In a school 75% students passed in Hindi and 82% students passed in English and 15% failed in both the subjects. If total number of passed candidates is 1872 then find the total number of students and also find failed students in Hindi.
Sol:-

total % of failed students = 10 + 15 + 3 = 28%
∴ total % of passed students = 100 – 28 = 72%
∴ 72% ⟶ 1872
      1% ⟶ 26
∴ total number of students = 100% = 2600        Answer

& number of failed students in Hindi = 25% = 25 × 26 = 650       Answer

203. Ramesh spends \(12\frac{1}{2}\% \) of his money and then he spends Rs. 1600. After this he spends 20% of the remaining and now left with Rs. 1200. Then find how much money he has initially?
Sol:-
Let initial money = x
\(\left( {x \times \frac{7}{8} – 1600} \right) \times \frac{4}{5} = 1200\)
x = \(\frac{{24800}}{7}\) Rs.         Answer

204. Present birth rate per thousand is 45 in a town and the death rate per thousands is 22. Find the net percentage increase in population.
Sol:-
Birth rate = 45 per thousand
Death rate == 22 per thousand
net increase in population = (45 – 22) per thousand
                                          = 23 per thousand
Hence required percentage = \(\frac{{23}}{{1000}} \times 100\)
= 23%         Answer

205. Amit gives 1% of his income to his two sons as pocket money every month. The amount received by the sons, 80% goes to elder son and he spends 80% of this amount. If he saves Rs. 40 per month. Find the income of Amit.
Sol:-

1 unit = 250
∴ income = 100 unit = 100 × 250 = 25000         Answer

206. An amount of 6100 Rs. is distributed among 8 men, 10 women and 12 children in such a way that a man gets 25% more than a woman and each woman gets 25% more than each child. Then find the amount received by each women.
Sol:-

∴ amount distributed among man, woman and children should be in the ratio 25 : 20 : 16
∴ men gets = 25x
   women gets = 20x
& child gets = 16x
∴ 8 × 25x + 10 × 20x + 12 × 16x = 20 × 10.304
= 206.08         Answer

207. In a school number of students increased by 20% this year. But the new law in the country made girls education free all over the country. So to collect the same amount as in the previous year the college management increased the fee of boys by 25%. Then find the ratio of boys in comparison with the girls this year.
Sol:-
Let last year students = S & Fees = F
∴ total Fee collected = SF
this year number of students = S + S × 20% = 1.25S
this year fees for boys = F + F × 25% = \(\frac{{5F}}{4}\) = 1.25f
total Fee this year = total Fee last year (Given)
∴ Number of boys = \(\frac{{SF}}{{1.25F}}\) = 0.85
∴ Girls = 0.45
∴ B : G = 2 : 1         Answer

208. A house costing Rs. 1464100 was constructed on a piece of land costing Rs. 291600. In what time will the cost of both be same if the cost of land is increasing by 10% annually while the cost of house is decreasing 10% annually?
Sol:-
Let after n years the price of both would be same
∴ \(1464100{\left( {1 – \frac{{10}}{{100}}} \right)^n} = 291600{\left( {1 + \frac{{10}}{{100}}} \right)^n}\)
⟹ \({\left( {\frac{9}{{10}}} \right)^n} = \frac{{2916}}{{14641}}{\left( {\frac{{11}}{{10}}} \right)^n}\)
⟹ \({\left( {\frac{9}{{11}}} \right)^n} = {\left( {\frac{9}{{11}}} \right)^4}\)
∴ n=4 years                Answer

209. Ankit gives 30% of his total income to his elder daughter and 40% of the remaining to his younger daughter. Then he distributes the remaining money in his three sons equally. If each son gets 812 Rs. then determine how much money did the elder daughter and younger daughter get?
Sol:-

∴ money of elder daughter = 30 × 58 = 1740 Rs.
& money of younger daughter = 28 × 58 = 1624 Rs.         Answer

210. A student scores 25% of the total marks and failed by 60 marks. Another student scores 50% of the total marks and thus gets 40 marks more than passing marks. Then by how much  percent the passing marks should be increased to get full marks in the exam?
Sol:-

∴ total marks = 100% = 400
∴ passing marks = 25% + 60
                               =  100 + 60 = 160
∴ \(160\left( {1 + \frac{x}{{100}}} \right)\) = 400
\(1 + \frac{x}{{100}} = \frac{5}{2}\)
\(\frac{x}{{100}} = \frac{3}{2}\)
∴ x = 150%          Answer

✅ Well done on completing Set 21!

Continue practising with Percentage Questions 211 to 220 → Set 22 or revisit the Percentage Concept Page to strengthen your formulas and tricks before moving ahead.

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