Ratio and Proportion Questions with Solutions | Set 1 (Q1 to Q10)

This set contains Ratio and Proportion Questions with Solutions — Set 1 (Q1 to Q10) 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.

1. Find the third proportion to the number 9 and 6.

2. Two numbers are in the ratio 3:7. If sum of these two numbers is 180, find the difference between the numbers.

3. If sum of three numbers is 171 and the ratio between the first and second be 3:5 and that between second and third be 4:5 then find the second number.

4. A bag contains an equal number of 50-paise, 25-paise, 20-paise coins. If the total amount is Rs. 60, how many coins of each type are there ?

5. The ratio of two numbers is 11:7. If each number be decreased by 3, the two numbers are in the ratio 5:3. Find the numbers.

6. The ratio of income of two persons is 7:4 and that of their expenditure is 3:5. Find the income of each person, if they save Rs. 460 and Rs. 230 respectively.

7. Divide Rs. 2160 into three parts in such a way that half of the first part, one-third of the second part and one-seventh of the third part are equal.

8. After an increament of 5 in both the numerator and denominator, a fraction changes to \(\frac{4}{5}\). Find the original fraction.

9.  The student in classes of a school are in the ratio 3:5:7. If 30 student are increased in each class, the ratio changes to 3:4:5. Find total number of students in each class before increase.

10. If \(\frac{1}{x}:\frac{1}{y}:\frac{1}{z}\) = 3:4:5 then find x : y : z.

1. Find the third proportion to the number 9 and 6.
Sol:
a = 9
b = 6

2. Two numbers are in the ratio 3:7. If sum of these two numbers is 180, find the difference between the numbers.
Sol:
(3 + 7) ⟶ 180
1 unit ⟶ 18
difference = 7 – 3 = 4 unit = 4 × 18 = 72       Answer

3. If sum of three numbers is 171 and the ratio between the first and second be 3:5 and that between second and third be 4:5 then find the second number.
Sol:
Let numbers be a, b, c
\(\frac{a}{b} = \frac{3}{5}\) ⟶ \(\frac{{3 \times 4}}{{5 \times 4}}\) ⟶ \(\frac{{12}}{{20}}\)
\(\frac{b}{c} = \frac{4}{5}\) ⟶ \(\frac{{4 \times 5}}{{5 \times 5}}\) ⟶ \(\frac{{20}}{{25}}\)
∴ (12 + 20 + 25) ⟶ 171
1 unit ⟶ 3
∴ second number = 20 unit = 20 × 3 = 60      Answer

4. A bag contains an equal number of 50-paise, 25-paise, 20-paise coins. If the total amount is Rs. 60, how many coins of each type are there ?
Sol:
x × (50 + 25 + 20 + 5) = 60 × 100
x = 60
So bag has 60 coins of each type           Answer

5. The ratio of two numbers is 11:7. If each number be decreased by 3, the two numbers are in the ratio 5:3. Find the numbers.
Sol:
Ratio of numbers = 11:7
Let first number = 11x
& second number = 7x
∴ \(\frac{{11x – 3}}{{7x – 3}} = \frac{5}{3}\) ⟹ x = 3
∴ numbers are:
11 × 3 = 33
& 7 × 3 = 21      Answer 

6. The ratio of income of two persons is 7:4 and that of their expenditure is 3:5. Find the income of each person, if they save Rs. 460 and Rs. 230 respectively.
Sol:
Income                   7      :      4
expenditure            3      :     5
saving               460 Rs.      230 Rs.
∴ \(\frac{{7x – 460}}{{4x – 230}} = \frac{3}{5}\)
35x – 2300 = 12x – 690
23x = 1610
x = 70
∴ Income are:
7 × 70 = 490 Rs.
4 × 70 = 280 Rs.          Answer 

7. Divide Rs. 2160 into three parts in such a way that half of the first part, one-third of the second part and one-seventh of the third part are equal.
Sol:
\(\frac{x}{2} = \frac{y}{3} = \frac{z}{7}\)
∴ x : y : z = 2 : 3 : 7 ⟶ (2 + 3 + 7) ⟶ 2160
                                             1 unit ⟶ 180
∴ x = 2 × 180 = 360 Rs.
y = 3 × 180 = 540 Rs.
z = 7 × 180 = 1260 Rs.         Answer 

8. After an increament of 5 in both the numerator and denominator, a fraction changes to \(\frac{4}{5}\). Find the original fraction.
Sol:
Let original fraction = \(\frac{x}{y}\)
∴ \(\frac{{x + 5}}{{y + 5}} = \frac{4}{5}\) ⟹ 5x = 4y – 5
So ratio of x & y can’t be determined.       Answer

9.  The student in classes of a school are in the ratio 3:5:7. If 30 student are increased in each class, the ratio changes to 3:4:5. Find total number of students in each class before increase.
Sol:

10. If \(\frac{1}{x}:\frac{1}{y}:\frac{1}{z}\) = 3:4:5 then find x : y : z.
Sol:
x : y : z = \(\frac{1}{3}:\frac{1}{4}:\frac{1}{5}\)
x : y : z = \(\frac{{60}}{3}:\frac{{60}}{4}:\frac{{60}}{5}\)
= 20 : 15 : 12   Answer

✅ Well done on completing Set 1!

Continue practising with Ratio and Proportion Questions 11 to 20 → Set 2 or revisit the Ratio and Proportion Concept Page to strengthen your formulas and tricks before moving ahead.

Consistent practice is the key to mastering ratio and proportion 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 Ratio on Wikipedia before attempting the next set.

This page is part of our complete series of ratio and proportion 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 ratio and proportion concept before your exam day.