Percentage Questions with Solutions — Set 18 (Q171 to Q180)

171. In a school there are 2700 students. Last day except 5% of the girls all the students were present in the school. Today except 4% of the boys all the students are present in the school, but in both the case the number of students present in the school were same. Then find the number of boys in the school.

172. A shopkeeper told the price of coffee by increasing 15% of the original cost. But customer insisted to decrease the price. So the shopkeeper sold it by decreasing the price by 15%. What is the loss or profit of shopkeeper & by how much percent?

173. In the previous government party q was in opposition. Now increasing the seats by 33.33% q is the ruling party and thus q enjoys twice the majority than that of party p in the previous government and the number of seats in the parliament be 500 and there were only two parties p and q then find the number of seats of the q in the new government.

174. A family’s ratio of saving to expenditure for the last month was 2 : 13. This month due to unforseen expenditure, saving fell to 50% of the amount saved last month. Salary, last month was Rs. 15000. This month there was increased of 20% in the salary. How much did the family spend this month?

175. The ratio of expenses to saving is 5 : 3 of a family. But the family’s expense is increased by 60% and the income increases by only 25%. Thus there is a deficit of Rs. 4000 in saving. Then find the increased income of the family.

176. Everyday a mango seller sells half his stock, 10% of the stock overnight gets spoiled. If 3305 mangoes rotted ovwe 3 nights then how many did he start with on the first day?

177. x% of the students of a class passed the exam. In the passed students y% are the girls and in the failed students z% are boys. Then find the percentage of passed boys over the failed girls.

178. A fraction is reduced such that when it is squared and then its numerator is increased by 25% and the denominator is reduced to 80% it result is \(\boldsymbol{\frac{5}{8}}\) of the original fraction. Then find the product of the numerator and denominator.

179. Selling price of a shirt and a coat is Rs. 4000. The cost price of shirt is 58.33% of the cost price of a coat and so amount of profit on both the shirt and coat is same, then the price of the shirt could be:
(i). 2100               (ii). 2552
(iii). 2100             (iv).1120

180. In an election onlhy two candidates contested. 20% of the voters did not vore and 120 votes were declared as invalid. The winners got 200 votes more than his opponents. Thus he secured 41% votes of the total voters on the voter list. Find the percentage votes of the defeated candidate out of the total votes casted.

171. In a school there are 2700 students. Last day except 5% of the girls all the students were present in the school. Today except 4% of the boys all the students are present in the school, but in both the case the number of students present in the school were same. Then find the number of boys in the school.
Solution:
b + g = 2700
b + 95%g = 96%b + g
\(\frac{{4b}}{{100}}\; =\; \frac{{5g}}{{100}}\)

∴ Number of boys = 5 × 300 = 1500          Answer

172. A shopkeeper told the price of coffee by increasing 15% of the original cost. But customer insisted to decrease the price. So the shopkeeper sold it by decreasing the price by 15%. What is the loss or profit of shopkeeper & by how much percent?
Solution:

Method(1):

∴ loss of 2.25%         Answer

Method(2):

15 – 15 – \(\frac{{15 \times 15}}{{100}}\)
= -2.25% i.e. loss of 2.25%         Answer

Method(3):

173. In the previous government party q was in opposition. Now increasing the seats by 33.33% q is the ruling party and thus q enjoys twice the majority than that of party p in the previous government and the number of seats in the parliament be 500 and there were only two parties p and q then find the number of seats of the q in the new government.
Solution:

majority means difference between the seats of parties according to question
(500 – 6x) × 2 = 8x – 500
1000 – 12x = 8x – 500
20x = 1500
x = 75
∴ Number of seats of q in new government = 4x = 4 × 75 = 300        Answer

174. A family’s ratio of saving to expenditure for the last month was 2 : 13. This month due to unforseen expenditure, saving fell to 50% of the amount saved last month. Salary, last month was Rs. 15000. This month there was increased of 20% in the salary. How much did the family spend this month?
Solution:

175. The ratio of expenses to saving is 5 : 3 of a family. But the family’s expense is increased by 60% and the income increases by only 25%. Thus there is a deficit of Rs. 4000 in saving. Then find the increased income of the family.
Solution:

∴ increased income = 4000 × 10 = 40000          Answer

176. Everyday a mango seller sells half his stock, 10% of the stock overnight gets spoiled. If 3305 mangoes rotted ovwe 3 nights then how many did he start with on the first day?
Solution:-
10% = \(\frac{1}{{10}}\)          &            \(\frac{1}{2}\)
take a number which is divisible by the denominator of three times \(\frac{1}{{10}}\) & 3 times \(\frac{1}{2}\)

Given that 661 ⟶ 3305
                    1 ⟶ 5
∴ mango in the first day = 8000 units
                                            = 8000 × 5 = 40000          Answer

177. x% of the students of a class passed the exam. In the passed students y% are the girls and in the failed students z% are boys. Then find the percentage of passed boys over the failed girls.
Solution:

∴ Required % = \(\frac{{Passed\;\;Boys}}{{Failed\;\;Girls}} \times 100\)
= \(\frac{{\frac{{x(100 – y)}}{{100}}}}{{\frac{{(100 – x)(100 – z)}}{{100}}}} \times 100\)
= \(\boldsymbol{\frac{{100x(100 – y)}}{{(100 – x)(100 – z)}}\%} \)          Answer

178. A fraction is reduced such that when it is squared and then its numerator is increased by 25% and the denominator is reduced to 80% it result is \(\boldsymbol{\frac{5}{8}}\) of the original fraction. Then find the product of the numerator and denominator.
Solution:
Let the original fraction be = \(\frac{x}{y}\)
∴ \(\frac{{{x^2} \times \frac{5}{4}}}{{{y^2} \times \frac{4}{5}}} = \frac{5}{8} \times \frac{x}{y}\) ⟹ \(\frac{x}{y} = \frac{2}{5}\)
∴ x×y = 2 × 5 = 10         Answer

179. Selling price of a shirt and a coat is Rs. 4000. The cost price of shirt is 58.33% of the cost price of a coat and so amount of profit on both the shirt and coat is same, then the price of the shirt could be:
(i). 2100               (ii). 2552
(iii). 2100             (iv).1120
Solution:
CP of shirt is 58.33% of CP of coat.
∴ ratio of CP of shirt and coat is 
58.33 : 100 = 7 : 12
selling price = cost price + profit
∴SP of shirt = 7x + y
SP of coat = 12x + y
Since the profit is same, so the selling price  of shirt will certainly be less than Rs. 2000 (Which is half of the total value) as it is clear that cost price of shirt is less than the cost price of coat.
Hence only possible option (d) is correct.            Answer

180. In an election onlhy two candidates contested. 20% of the voters did not vore and 120 votes were declared as invalid. The winners got 200 votes more than his opponents. Thus he secured 41% votes of the total voters on the voter list. Find the percentage votes of the defeated candidate out of the total votes casted.
Solution:

votes of defeated candidate = 39 × 40 – 120 = 1440
total votes casted = 80 × 40 = 3200
∴ required % = \(\frac{{1440}}{{3200}} \times 100\)
= 45%        Answer

✅ Well done on completing Set 18!

Continue practising with Percentage Questions 181 to 190 → Set 19 or revisit the Percentage Concept Page to strengthen your formulas and tricks before moving ahead.

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