Practice Questions
Concept Explanation
A ratio compares two quantities of the same kind by division. Written as a : b, it tells us how many times one quantity contains the other — not their absolute values.
Key Properties
- Order matters: a : b is generally not equal to b : a.
- Same units: Convert both quantities to the same unit before forming a ratio.
- Simplest form: Divide both terms by their HCF. Example: 24 : 36 = 2 : 3.
- No unit in the final ratio: Units cancel when both terms share the same unit.
Part-to-Part vs Part-to-Whole
If boys : girls = 4 : 5, the whole class has 4 + 5 = 9 equal parts. Boys are 4/9 of the total and girls are 5/9 of the total.
Converting Ratio to Actual Numbers
If a : b = 3 : 5, write the quantities as 3k and 5k for some constant k. Use the given total, difference, or one actual value to find k.
Example: Ratio 3 : 5 and total 40 → 3k + 5k = 40 → k = 5 → numbers are 15 and 25.
Three-Term Ratios
For a : b : c, use ak, bk, and ck. Sum of parts = (a + b + c)k.
Placement Shortcut
To divide amount M in ratio a : b, first share = M × a/(a + b) and second share = M × b/(a + b).
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Q1 Easy
What is the ratio 24 : 36 in simplest form?
ExplanationHCF of 24 and 36 is 12. Dividing both terms: 24/12 : 36/12 = 2 : 3. -
Q2 Easy
Express the ratio of 45 minutes to 2 hours in simplest form.
Explanation2 hours = 120 minutes. Ratio = 45 : 120 = 3 : 8 after dividing by 15. -
Q3 Easy
Two quantities are in the ratio 2 : 3. If their total is 50, what is the smaller quantity?
ExplanationLet quantities be 2k and 3k. Then 5k = 50, so k = 10. Smaller quantity = 2k = 20. -
Q4 Medium
Divide Rs. 120 in the ratio 3 : 5. What is the larger share?
ExplanationTotal parts = 8. Larger share = 120 × 5/8 = Rs. 75. -
Q5 Medium
The ratio of boys to girls in a class is 4 : 5. If the total number of students is 108, how many girls are there?
ExplanationGirls correspond to 5 parts out of 9. Girls = 108 × 5/9 = 60. -
Q6 Easy
What is 15 : 25 in simplest form?
ExplanationDivide both terms by 5: 15 : 25 = 3 : 5. -
Q7 Easy
If a : b = 5 : 7 and b = 28, what is the value of a?
ExplanationFrom 5/7 = a/28, we get a = (5 × 28)/7 = 20.
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Q8 Medium
Two numbers are in the ratio 7 : 9 and their sum is 128. What is the smaller number?
Explanation7k + 9k = 128 → k = 8. Smaller number = 7k = 56. -
Q9 Medium
An amount is divided in the ratio 1 : 2 : 3. If the total is Rs. 360, what is the middle share?
ExplanationMiddle share gets 2 parts out of 6. Share = 360 × 2/6 = Rs. 120. -
Q10 Medium
Rs. 840 is divided between A and B in the ratio 4 : 3. How much does B receive?
ExplanationB gets 3 parts out of 7. Amount = 840 × 3/7 = Rs. 360. -
Q11 Hard
Three numbers are in the ratio 2 : 3 : 5. If the largest number exceeds the smallest by 36, what is the largest number?
ExplanationNumbers are 2k, 3k, 5k. Difference 5k − 2k = 3k = 36 → k = 12. Largest = 5k = 45. -
Q12 Medium
What is the ratio of 2.5 to 0.5 in simplest form?
Explanation2.5 : 0.5 = 25 : 5 = 5 : 1 after multiplying by 10 and simplifying. -
Q13 Hard
Two quantities are in the ratio 3 : 4. If the first quantity is doubled and the second remains unchanged, what is the new ratio?
ExplanationOriginal quantities 3k and 4k. After doubling the first: 6k and 4k → ratio 6 : 4 = 3 : 2. -
Q14 Easy
Red and blue beads are in the ratio 5 : 3. If there are 64 beads in all, how many are red?
ExplanationRed beads = 64 × 5/8 = 40.
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DS1 Easy
What is the first number in the ratio?
Statement IThe two numbers are in the ratio 3 : 4 and their sum is 98.
Statement IIThe second number exceeds the first by 14.
ExplanationStatement I: 3k + 4k = 98 → k = 14 → first number = 42. Statement II: 4k − 3k = 14 → k = 14 → first number = 42. Each alone is sufficient. -
DS2 Medium
What is the ratio of the two quantities in simplest form?
Statement IThe quantities are 48 and 72.
Statement IIThe HCF of the two quantities is 24.
ExplanationStatement I alone gives 48 : 72 = 2 : 3. Statement II gives the HCF but not the actual quantities, so the ratio cannot be fixed.
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DS3 Medium
What is the total of the two quantities?
Statement IThe quantities are in the ratio 2 : 3.
Statement IIThe difference between the quantities is 15.
ExplanationLet the quantities be 2k and 3k. Statement I alone does not fix k. Statement II alone (difference 15) fits many pairs such as 20 and 5, or 18 and 3. Together: 3k − 2k = 15 → k = 15, total = 5k = 75. -
DS4 Hard
Is the ratio of the first quantity to the second greater than 1 : 1?
Statement IThe first quantity is 56.
Statement IIThe second quantity is 48.
ExplanationEach statement alone gives only one quantity. Together, ratio = 56 : 48 = 7 : 6, which is greater than 1 : 1.