Percentage Questions with Solutions — Set 19 (Q181 to Q190)

181. Ankit consumes 25kg of rice and 9 kg of wheat. The price of rice is 20% of the price of wheat and thus he spends total Rs. 350 on the rice and whear per month. If the price of wheat is increased by 20% then what is the percentage reduction of rice consumption for the same expenditure of Rs. 350? Given that the price of rice and consumption of wheat is constant.

182. In an election only two candidate contested. 15% of the voters did not vote and 41 votes were invalid. The elected contestant got 314 votes more than the other candidate. If the elected candidate got 45% of the total votes in the voting list. Then find the individual votes of each candidate.

183. A man lost 50% of his initial capital in the gambling after playing 3 rounds. The rule of the gambling is that if he winds, he will receive Rs. 200 but he has to give 50% of the total amount after each round. Luckily he won all the three rounds. The initial amount with which he had started the gambling was how much?

184. A, B, C and D purchased a restaurant for Rs. 56 lakhs. The contribution of B, C and D together is 460% that of A, alone. The contribution of A, C and D together is 366.66% that of B’s contribution and the contribution of C is 40% that of A, B and D together. Then find the amount contributed by D?

185. In a village, three people contested for the post of village pradhan. Due to their own interest, all the voters voted and no vote was invalid. The losing candidate got 30% votes. What could be the minimum absolute margin of votes by which the winning candidate led by the nearest rival, if each candidate got an integral percent of votes?

186. The pressure of a definite mass of a gas is directly proportional to temperature and inversely proportional to the volume under the given conditions. If the temperature is increased by 60% and the volume is decreased by 20% then find by what % new pressure is increased/decreased?

187. The price of a jewellery first increases by x% and the new price decreased by x%. After one such up and down cycle, the price of a jewellery decreased by Rs. 26025. After a second updown cycle the jewellery was sold for Rs. 599616. What was the original price of the jewellery?

188. If the price of rice  has been increased by 10% and the price of other commodities is increased by 15%. If the ratio of expenditure on rice and other commodities of a person be 2 : 5 and his salary be Rs. 3500. Then how many rupees his salary be increased so that he can consume the same quantity as before?

189. Three shopkeeper promised to sell their goods at the marked price. A gives two successive discount of 25% and 15% and B gives two successive discount of 10% and 30% while C gives a single discount of 36%.Whose scheme is best for the customer?

190. A man orders 4 pairs of black shoes and some pairs of brown shoes. The price of black pair is double that of brown pair. While billing the clerk interchanged the number of pair of black and brown shoes and hence the total amount of bill increased by 50%. Find the ratio of pair of black and brown shoes initially.

181. Ankit consumes 25kg of rice and 9 kg of wheat. The price of rice is 20% of the price of wheat and thus he spends total Rs. 350 on the rice and whear per month. If the price of wheat is increased by 20% then what is the percentage reduction of rice consumption for the same expenditure of Rs. 350? Given that the price of rice and consumption of wheat is constant.
Solution:-
Price of wheat = x
∴ price of rice = 20% of x = \(\frac{x}{5}\)
∴ 25 × \(\frac{x}{5}\) + 9 × x = 350
14x = 350
x = 25 ⟵ Price of wheat
& price of rice = 5
increased price of wheat = 25 + 20% × 25 = 30
∴ 30 × 9 + 5 × y = 350
⟹ y = 16 ⟵ New consumption of rice
∴ required % reduction = \(\frac{{25 – 16}}{{25}} \times 100\) = 36%         Answer

182. In an election only two candidate contested. 15% of the voters did not vote and 41 votes were invalid. The elected contestant got 314 votes more than the other candidate. If the elected candidate got 45% of the total votes in the voting list. Then find the individual votes of each candidate.
Solution:-

∴ votes of winner = 45 × \(\frac{{273}}{5}\) = 2457            Answer
& votes of Loser = 40 × \(\frac{{273}}{5}\) – 41 = 2143          Answer

∴ votes of winner = 45 × \(\frac{{273}}{5}\) = 2457            Answer
& votes of Loser = 40 × \(\frac{{273}}{5}\) – 41 = 2143            Answer

183. A man lost 50% of his initial capital in the gambling after playing 3 rounds. The rule of the gambling is that if he winds, he will receive Rs. 200 but he has to give 50% of the total amount after each round. Luckily he won all the three rounds. The initial amount with which he had started the gambling was how much?
Solution:-
Let the initial amount = x

184. A, B, C and D purchased a restaurant for Rs. 56 lakhs. The contribution of B, C and D together is 460% that of A, alone. The contribution of A, C and D together is 366.66% that of B’s contribution and the contribution of C is 40% that of A, B and D together. Then find the amount contributed by D?
Solution:-
A + B + C + D = 56 ………….(ii)
       B + C + D = 4.6A ………..(iii)
       A + C + D = \(\frac{{11}}{3}B\) ………..(iii)
       A + B + D = 2.5C …………(iv)

using equation(i) & (ii) ⟹ A = 16
using equation (i) & (iv) ⟹ C = 16
using equation (i) & (ii) ⟹ B = 12
∴ D=18 lakh          Answer

185. In a village, three people contested for the post of village pradhan. Due to their own interest, all the voters voted and no vote was invalid. The losing candidate got 30% votes. What could be the minimum absolute margin of votes by which the winning candidate led by the nearest rival, if each candidate got an integral percent of votes?
Solution:-

186. The pressure of a definite mass of a gas is directly proportional to temperature and inversely proportional to the volume under the given conditions. If the temperature is increased by 60% and the volume is decreased by 20% then find by what % new pressure is increased/decreased?
Solution:-

\({P_{new}} = \frac{{K\frac{{16}}{{10}}T}}{{\frac{8}{{10}}V}} = K \times 2\frac{T}{V}\)
∴ Required % = \(\frac{{2 \boldsymbol{-} 1}}{1} \times 100\) = 100% ↑       Answer

187. The price of a jewellery first increases by x% and the new price decreased by x%. After one such up and down cycle, the price of a jewellery decreased by Rs. 26025. After a second updown cycle the jewellery was sold for Rs. 599616. What was the original price of the jewellery?
Solution:-
Let original price of jewellery = p
∴ Iˢᵗ cycle net % change = x – x – \(\frac{{{x^2}}}{{100}}\)
= \(\frac{{{x^2}}}{{100}}\% \) ↓
Case(i):
P.\(\frac{{{x^2}}}{{{{100}^2}}}\) = 26025 …………..(i)

Case(ii):
\(P\left( {1 + \frac{x}{{100}}} \right)\left( {1 – \frac{x}{{100}}} \right)\left( {1 + \frac{x}{{100}}} \right)\left( {1 – \frac{x}{{100}}} \right) = 599616\)
⟹ \(P{\left( {1 – \frac{{{x^2}}}{{{{100}^2}}}} \right)^2} = 599616\) ……………(ii)
on dividing equation (ii) by (i)
\(\frac{{{{\left( {1 – \frac{{{x^2}}}{{{{100}^2}}}} \right)}^2}}}{{\frac{{{x^2}}}{{{{100}^2}}}}} = \frac{{5996165}}{{26025}} = 23.04 = \frac{{2304}}{{100}}\)
⟹ \(\frac{{1 – \frac{{{x^2}}}{{{{100}^2}}}}}{{\frac{x}{{100}}}} = \sqrt {\frac{{2304}}{{100}}} = \frac{{48}}{{10}} = \frac{{24}}{5}\)
Let \(\frac{x}{{100}} = y\)
⟹ \(\frac{{1 \boldsymbol{-} {y^2}}}{y} = \frac{{24}}{5}\) ⟹ y = \(\frac{1}{5}\) = \(\frac{x}{{100}}\)
∴ 5y² + 24y – 5 = 0 ⟹ y = \(\frac{1}{5}\) = \(\frac{x}{{100}}\)
∴ x = 20% ⟹ \(P.\frac{{{x^2}}}{{{{100}^2}}} = 26025\) ⟹ P = 650625           Answer

188. If the price of rice  has been increased by 10% and the price of other commodities is increased by 15%. If the ratio of expenditure on rice and other commodities of a person be 2 : 5 and his salary be Rs. 3500. Then how many rupees his salary be increased so that he can consume the same quantity as before?
Sol:-

Hence total ↑ expenditure = 100 + 375 = 475
So his salary must be increased by 475 Rupees.         Answer

189. Three shopkeeper promised to sell their goods at the marked price. A gives two successive discount of 25% and 15% and B gives two successive discount of 10% and 30% while C gives a single discount of 36%.Whose scheme is best for the customer?
Solution:-
Single equivalent discount of A = 25 + 15 – \(\frac{{25 \times 15}}{{100}}\) = 36.25%
Single equivalent discount of B = 10 + 30 – \(\frac{{10 \times 30}}{{100}}\) = 37^
& discount of C = 36%
∴ B’s discount is best for customer       Answer

190. A man orders 4 pairs of black shoes and some pairs of brown shoes. The price of black pair is double that of brown pair. While billing the clerk interchanged the number of pair of black and brown shoes and hence the total amount of bill increased by 50%. Find the ratio of pair of black and brown shoes initially.
Solution:-

∴ total cost = 8y + xy
while billing:

new total cost = 2xy + 4y
Given ⟹ 2xy + 4y = 8y + xy + \(\frac{{8y + xy}}{2}\)
⟹ 4xy + 8y = 16y + 2xy + 8y + xy
⟹ xy = 16y
      x = 16
∴ Ratio of            Black shoes : Brown shoes 
                                                4  :   16
                                                1  :   4         Answer

✅ Well done on completing Set 19!

Continue practising with Percentage Questions 191 to 200 → Set 20 or revisit the Percentage Concept Page to strengthen your formulas and tricks before moving ahead.

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