Percentage Questions with Solutions — Set 22 (Q211 to Q220)

211. The ratio of the boys and girls sitting in an examination is 16 : 9. The ratio of boys and girls that passed the exam is 4 : 3. If 75% girls passed in the exam then find the % of boys and find the total % of students that passed in the exam.

212. A survey was carried out on x number of people of an institution reveals that 60% people drink coffee and when survey was carried out on the other extra y number of people of sasme institution, then it was found that all the people drink coffee. Then it was also found that 70% of both types of people x and y drinks coffee. Find out x is what % of y?

213. Ankit deposits some money in the bank. He invested 150% of it in stocks and 25% more than amount deposited in bank invested in bonds. At the end of a year, he made some income from the above investments which is 12.5% of the money deposited in bank, \(6\frac{1}{4}\% \) of amount invested in stocks and 5% of the amount invested in bonds. Out of the total income he made, he spent again 60% to buy the shares of a company. If he saves Rs. 180000 from his total income, then find the amount of money he invested initially in stocks?

214. It is necessary to obtain 40% marks to pass the exam. A obtains 10% less marks than pass marks. B obtains \(11\frac{1}{9}\% \) less marks than A, and C obtains \(41\frac{3}{17}\% \) less marks than A & B. Then find if C qualifies the exam or not?

215. If the wage of a labour is increased by \(12\frac{1}{2}\% \) and the work hour of the labour are decreased by 8%. Earlier he works 50 hours a week and thus earns Rs. 1200 as wages. Find out his new wage per week and % increase in his weekly wages.

216. When x litres of oil is poured into a vessel then y% vessel remains empty. How much more oil must be poured into the vessel so that the vessel will be filled completely and also find the capacity of the vessel?

217. Two students appeared at an examination. One of them secured 9 marks more than the other and his marks were 56% of the sum of their marks. Find the marks obtained by them.

218. In a school 35% of the students play cricket and 50% play badminton. If 20% of the students neither play cricket nor badminton then find the % of playing students?

219. A labour earns Rs. 2400 in 60 days in a mill. Later on his wages are increased by 10% and his work days are reduced by 15%. Find how much money more or less as compared to initial situation, the labour will get now?

220. The monthly salary of Ankit is Rs. 5000 and he spends on cloths and food in the ratio 2 : 5. If the price of clothes increased by 10% and expenditure on food increased by 20% then by how much % his monthly income should be increased so that his consumption will remain unchanged?

211. The ratio of the boys and girls sitting in an examination is 16 : 9. The ratio of boys and girls that passed the exam is 4 : 3. If 75% girls passed in the exam then find the % of boys and find the total % of students that passed in the exam.
Sol:-

3y = 75% × 9x ⟹ \(\frac{x}{y} = \frac{4}{9}\)
∴ % of passed boys = \(\frac{{4y}}{{16x}} \times 100\) = \(\frac{4}{{16}} \times \frac{9}{4} \times 100\) = 56.25%         Answer
& % of passed students = \(\frac{{4y + 3y}}{{16x + 9x}} \times 100 = \frac{7}{{25}} \times \frac{9}{4} \times 100\) = 63%      Answer

212. A survey was carried out on x number of people of an institution reveals that 60% people drink coffee and when survey was carried out on the other extra y number of people of sasme institution, then it was found that all the people drink coffee. Then it was also found that 70% of both types of people x and y drinks coffee. Find out x is what % of y?
Sol:-

∴ \(\frac{x}{y} \times 100 = \frac{3}{{10}} \times 100\) = 300%         Answer

213. Ankit deposits some money in the bank. He invested 150% of it in stocks and 25% more than amount deposited in bank invested in bonds. At the end of a year, he made some income from the above investments which is 12.5% of the money deposited in bank, \(\boldsymbol{6\frac{1}{4}\%} \) of amount invested in stocks and 5% of the amount invested in bonds. Out of the total income he made, he spent again 60% to buy the shares of a company. If he saves Rs. 180000 from his total income, then find the amount of money he invested initially in stocks?
Sol:-
Let amount deposited in bank = 100
∴ amount invested in stocks = 150
amount invested in bonds = 100 + 25 = 125
∴ income from bank = 12.5% × 100 = \(\frac{{25}}{2}\)
income from stocks  = \(6\frac{1}{4}\% \) × 150 = \(\frac{{75}}{8}\)
income from bonds = 5% × 125 = \(\frac{{25}}{4}\)
∴ total income = \(\frac{{25}}{2} + \frac{{75}}{8} + \frac{{25}}{4} = \frac{{225}}{8}\)
Saving from this income = \(\frac{{225}}{8} \times 40\% = \frac{{45}}{4}\)
∴ \(\frac{{45}}{4}\) ⟶ 180000
1 unit ⟶ 16000
∴ amount invested in stock = 150 unit
                                            = 150 × 16000
                                            = 2400000             Answer

214. It is necessary to obtain 40% marks to pass the exam. A obtains 10% less marks than pass marks. B obtains \(\boldsymbol{11\frac{1}{9}\%} \) less marks than A, and C obtains \(\boldsymbol{41\frac{3}{17}\%} \) less marks than A & B. Then find if C qualifies the exam or not?
Sol:-
Let total marks of exam = 100
∴ Passing marks = 40% × 100 = 40
 A’s marks = 40 × 90% = 36
B’s marks = 36 × \(\frac{8}{9}\)
C’s marks = (36 + 32) × \(\frac{10}{17}\) = 40
Hence C obtains passing marks
∴ C will pass the exam.               Answer

215. If the wage of a labour is increased by \(\boldsymbol{12\frac{1}{2}\%} \) and the work hour of the labour are decreased by 8%. Earlier he works 50 hours a week and thus earns Rs. 1200 as wages. Find out his new wage per week and % increase in his weekly wages.
Sol:-

∴ % ↑ in total wages = \(\frac{7}{{200}} \times 100\) = 3.5%         Answer
& new wage per week = 207 × 6 = 1242         Answer

216. When x litres of oil is poured into a vessel then y% vessel remains empty. How much more oil must be poured into the vessel so that the vessel will be filled completely and also find the capacity of the vessel?
Sol:-
     x ⟶ (100 – y)%
⟹ 1% ⟶ \(\frac{x}{{100 – y}}\)
∴ 100% ⟶ \(\frac{{100x}}{{100 \boldsymbol{-} y}}\)
∴ capacity of vessel = \(\boldsymbol{\frac{{100x}}{{100 – y}}}\)        Answer

Since after pouring x litre oil y% vessel remain empty.
So more oil required to fill the vessel = y% of its capacity
= \(\frac{y}{{100}} \times \frac{{100x}}{{100 \boldsymbol{-} y}}\) = \(\boldsymbol{\frac{{xy}}{{100 \boldsymbol{-} y}}}\)          Answer

217. Two students appeared at an examination. One of them secured 9 marks more than the other and his marks were 56% of the sum of their marks. Find the marks obtained by them.
Sol:-
Let marks of first student = x
& marks of second student = y
x = y + 9 ⟹ x – y = 9 …………(i)
& \(x = \frac{{56}}{{100}}(x + y)\) ⟹ \(\frac{{56}}{{100}}(1 + \frac{y}{x}) = 1\)
⟹ \(\frac{x}{y} = \frac{{14}}{{11}}\) …………..(ii) 
 ⟹ From equation (ii):
x – y = 3 unit ⟶ 9
            1 unit ⟶ 3
∴ x = 14 × 3 = 42
   y = 11 × 3 = 33         Answer

218. In a school 35% of the students play cricket and 50% play badminton. If 20% of the students neither play cricket nor badminton then find the % of playing students?
Sol:-

∴ % of playing students = 100 – (45 + 20 + 30)
                                      = 5%          Answer

219. A labour earns Rs. 2400 in 60 days in a mill. Later on his wages are increased by 10% and his work days are reduced by 15%. Find how much money more or less as compared to initial situation, the labour will get now?
Sol:-

220. The monthly salary of Ankit is Rs. 5000 and he spends on cloths and food in the ratio 2 : 5. If the price of clothes increased by 10% and expenditure on food increased by 20% then by how much % his monthly income should be increased so that his consumption will remain unchanged?
Sol:-
Total salary = 5000
∴ money spent on food = \(\frac{5}{7} \times 5000\)
money spent on cloths = \(\frac{2}{7} \times 5000\)
increased expenditure on cloths = \(\frac{2}{7} \times 5000 \times \frac{{120}}{{100}}\)
total expenditure now = \(\frac{{2 \times 5000 \times 110 + 5 \times 5000 \times 120}}{{700}}\)
= \(\frac{{41000}}{7}\)
∴ increase in salary = \(\frac{{41000}}{7} \;-\; 5000\)
= \(\frac{{6000}}{7}\)
∴ % ↑ in salary = \(\frac{{6000}}{{7 \times 5000}} \times 100\) = \(\boldsymbol{17\frac{1}{7}\%} \)           Answer

Alternately: In such type of questions assume value of salary as per your requirement to save your valuable time.

new salary = 820
∴ % ↑ in salary = \(\frac{{820 \;-\; 700}}{{700}} \times 100\)
                        = \(\boldsymbol{17\frac{1}{7}\%} \)      Answer 

✅ Well done on completing Set 22!

Continue practising with Percentage Questions 221 to 227 → Set 23 or revisit the Percentage Concept Page to strengthen your formulas and tricks before moving ahead.

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