This set contains Percentage Questions with Solutions — Set 23 (Q221 to Q227) covering a mix of question types and difficulty levels — from basic to advanced — exactly as asked in real competitive exams.
Solutions are written in a simple, step-by-step notebook style for easy self-study and quick understanding. Each solution is broken down step by step so even the toughest question feels easy. These questions are hand-picked for students preparing for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and all campus placement aptitude tests. International students preparing for GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests will find these equally useful.
✏️ Attempt each question on your own first — then check the solution below.
Percentage Questions 221 to 227 with Solutions
221. In a two digit positive number, the digit in the unit place is equal to the square of the digit in ten’s place, and the difference between the number and the number obtained by interchanging the digits is 54. What is 60% of the original number?
222. Shelf A has \(\frac{4}{5}\) of the number of books that the shelf B has. If 25% of the books in A are transfered to B and then 25% of the books from B are transfered to A, then find the % of the total number of books that A will have.
223. 500 kg of ore contained a certain amount of iron. After the blast furnace process 200 kg of slag containing \(12\frac{1}{2}\% \) of iron was removed. The % of iron in the remaining ore was found to be 20% more than the % in the original ore. How many kg of iron was there in the original 500 kg ore?
224. In an election, involving two candidates, 68 votes were declared invalid. The winner candidate secured 52% of the total valid votes and win by 96 votes. Then find the total number of votes?
225. A, B, C and D purchased an Hotel 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?
226. The pressure of definite mass of gas is directly proportional to the temperature and inversely proportional to the volume under the given conditions. If temperature is increased by 60% and the volume is decreased by 20% then find by how much % new pressure will ↑/↓.
227. Arpit and Sanjay are sharing a flat, with an arrangement of equally dividing the household expenses. Arpit went to delhi, where a sale was going on and bought umbrella for house worth 150 on 20% discount but he lost it on his way back and had to pay new one. How much did he end up spending on the umbrellas.
Solutions — Percentage Questions 221 to 227
221. In a two digit positive number, the digit in the unit place is equal to the square of the digit in ten’s place, and the difference between the number and the number obtained by interchanging the digits is 54. What is 60% of the original number?
Sol:-
Let number = xy
y = x² …………..(i)
(10x + y) -(10y + x) = -54
9x – 9y = -54
x – y = -6 …………(ii)
⟹ x – x² = -6
⟹ x² -x – 6 = 0
x = 3
∴ y = 9
Hence Number = 39
∴ 60% of 39 = \(\frac{{60}}{{100}} \times 39\) = 23.4 Answer
222. Shelf A has \(\boldsymbol{\frac{4}{5}}\) of the number of books that the shelf B has. If 25% of the books in A are transfered to B and then 25% of the books from B are transfered to A, then find the % of the total number of books that A will have.
Sol:-
Let shelf of B has 5x books
∴ number of books in shelf A = \(\frac{4}{5} \times 5x\) = 4x
now number of books in shelf B after transfer = 5x + 25% × 4x = 6x
now number of books in shelf A = (4x – x) = 25% × 6x
= \(3x + \frac{{3x}}{2} = \frac{{9x}}{2}\)
∴ required % = \(\frac{{\frac{{9x}}{2}}}{{9x}} \times 100\) = 50% Answer
223. 500 kg of ore contained a certain amount of iron. After the blast furnace process 200 kg of slag containing \(\boldsymbol{12\frac{1}{2}\%} \) of iron was removed. The % of iron in the remaining ore was found to be 20% more than the % in the original ore. How many kg of iron was there in the original 500 kg ore?
Sol:-
Let original iron in 500 kg ore = x kg
iron in slag = 200 × \(12\frac{1}{2}\% \) = 200 × \(\frac{1}{8}\) = 25 kg
\(\frac{{x \;-\; 25}}{{300}} = \frac{x}{{500}} \times 1.2\)
⟹ 3.6x = 5x – 125
1.4x = 125
x = 89.28 kg Answer
224. In an election, involving two candidates, 68 votes were declared invalid. The winner candidate secured 52% of the total valid votes and win by 96 votes. Then find the total number of votes?
Sol:-
Let total valid votes = 100
∴ total votes of winner = 525
& total votes of loser = 48
∴ winner wins by 52 – 48 = 4 votes
Here it is given:
4 ⟶ 96
1 ⟶ 24
∴ total valid votes = 2400
& total invalid votes = 68
∴ total votes = 2400 + 68 = 2468 Answer
225. A, B, C and D purchased an Hotel 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?
Sol:-
A + B + C + D = 56 ………..(i)
B + C + D = 4.6A
⟹ A + 4.6A = 56 ⟹ A = 10
A + C + D = \(\frac{{11}}{3}B\) ⟹ B + \(\frac{{11}}{3}B\) = 56 ⟹ B = 12
0.4(A + B + D) = C ⟹ A + B + D = \(\frac{5}{2}C\)
⟹ C + \(\frac{5}{2}C\) = 56 ⟹ C = 16
∴ D = 56 – (10 + 12 + 16) = 18 lakh Answer
226. The pressure of definite mass of gas is directly proportional to the temperature and inversely proportional to the volume under the given conditions. If temperature is increased by 60% and the volume is decreased by 20% then find by how much % new pressure will ↑/↓?
Sol:-
\(\displaystyle P \propto \frac{T}{V}\) ⟹ \(\displaystyle P = K.\frac{T}{V}\)
∴ new pressure = \(\frac{{2 – 1}}{1} \times 100\) = 100% ↑ Answer
227. Arpit and Sanjay are sharing a flat, with an arrangement of equally dividing the household expenses. Arpit went to delhi, where a sale was going on and bought umbrella for house worth 150 on 20% discount but he lost it on his way back and had to pay new one. How much did he end up spending on the umbrellas.
Sol:-
Expenditure by Arpit on umbrellas = 150 × 80% + \(\frac{{150}}{2}\)
= 195 Rs. Answer
✅ Well done on completing Set 23!
Now revisit the Percentage Concept Page to strengthen your formulas and tricks before moving ahead.
Consistent practice is the key to mastering percentage for SSC CGL, SSC CHSL, CAT, Bank PO, Bank Clerk, UPSC CSAT, Railway RRB, AMCAT, eLitmus, TCS NQT and international exams including GRE, GMAT, SAT, ACT, MAT and all Numerical Reasoning Tests. Want to understand the concept better? Read about Percentage on Wikipedia before attempting the next set.
This page is part of our complete series of percentage questions with solutions for competitive exams — covering every question type from basic to advanced so you can build speed, accuracy and confidence. Practising these questions regularly will also strengthen your core percentage concept before your exam day.
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