Proportional Reasoning-1 — Quiz

Q1. Sunita argues that image B (80 mm by 60 mm) is similar to image A (60 mm by 40 mm) because in both, height is 20 mm less than width. Which conclusion follows from the chapter's definition of proportional change?

• A. Sunita is right because the difference is the same in both images.
• B. Sunita is wrong because image B is taller than image A.
• C. Sunita is right only if both images are printed on the same paper.
• D. Sunita is wrong because proportionality means change by the same factor, not the same difference.

Q2. Image A has width 60 mm and height 40 mm. Image D has width 90 mm and height 60 mm. Rohit wants to check whether D's dimensions are proportional to A's. Which factor links them?

• A. Both width and height of D are A's measurements multiplied by 3/2.
• B. Both width and height of D are A's measurements with 30 mm added.
• C. Width is multiplied by 3/2 but height is multiplied by 2.
• D. Width is increased by 30 mm and height is increased by 20 mm.

Q3. A market shop sold 600 ml of orange juice and 900 ml of apple juice in a morning. Geeta writes the ratio of orange juice to apple juice in its simplest form. What does she write?

• A. 6 : 9
• B. 1 : 1.5
• C. 3 : 2
• D. 2 : 3

Q4. Anjali reduces 90 : 60 to simplest form by dividing both terms by their HCF. Which step is correct?

• A. HCF is 10, so 90 : 60 = 9 : 6.
• B. HCF is 15, so 90 : 60 = 6 : 4.
• C. HCF is 30, so 90 : 60 = 3 : 2.
• D. HCF is 60, so 90 : 60 = 1.5 : 1.

Q5. Meera reads the chapter and says: 'Two ratios are proportional only when their simplest forms are identical.' Which option correctly evaluates her statement?

• A. She is wrong; identical simplest forms are not needed.
• B. She is wrong; two ratios are proportional whenever their sums are equal.
• C. She is right only if both ratios start with the same first term.
• D. She is right; this is the definition the chapter uses.

Q6. Vikram is checking whether 4 : 7 :: 12 : 21 is true. He reduces 12 : 21 to its simplest form. Which conclusion is correct?

• A. 12 : 21 simplifies to 4 : 7, so the proportion is true.
• B. 12 : 21 simplifies to 6 : 7, so the proportion is false.
• C. 12 : 21 is already in simplest form, so the proportion is false.
• D. 12 : 21 simplifies to 3 : 7, so the proportion is false.

Q7. Manish writes 8 : 3 :: 24 : 6 and asks his teacher if it is true. The teacher reduces 24 : 6 first. Which statement correctly explains the answer?

• A. It is true because 24 = 8 × 3 and 6 = 3 × 2.
• B. It is false because 8 + 3 is not equal to 24 + 6.
• C. It is true because both ratios are proper fractions.
• D. It is false because 24 : 6 simplifies to 4 : 1, not 8 : 3.

Q8. Find the missing second term in 14 : 21 :: 28 : ____ so that the ratios are proportional.

• A. 35
• B. 49
• C. 42
• D. 56

Q9. When Neelima was 3 years old, her mother was 30. Nine years later, Neelima is 12 and her mother is 39. Salim claims the ratio of their ages is still 1 : 10. Which conclusion follows?

• A. Salim is right; adding 9 to both keeps the ratio.
• B. Salim is wrong; the new ratio is 1 : 3.
• C. Salim is right; ages always stay in the same ratio.
• D. Salim is wrong; the new ratio is 4 : 13, not 1 : 10.

Q10. Ravi claims: 'If I add 5 to both terms of the ratio 2 : 3, the ratio does not change.' Which step shows his claim is wrong?

• A. 2 + 5 = 7 and 3 + 5 = 8, and 7 : 8 has simplest form 2 : 3.
• B. Ratios always stay the same under addition; the chapter agrees with Ravi.
• C. Both 2 and 3 become 10, so the ratio becomes 1 : 1.
• D. 2 + 5 = 7 and 3 + 5 = 8, and 7 : 8 is already in simplest form, not 2 : 3.

Q11. Aryabhata's Rule of Three uses four quantities — pramana, phala, ichchha and ichchhaphala. In a problem of the form a : b :: c : ?, what does the missing fourth term ichchhaphala represent?

• A. The known result corresponding to pramana.
• B. The known argument set up first in the proportion.
• C. The unknown result corresponding to ichchha.
• D. The HCF used to simplify the ratio.

Q12. A car travels 90 km in 150 minutes at constant speed. Using the Rule of Three, how far will it travel in 4 hours?

• A. 120 km
• B. 150 km
• C. 240 km
• D. 144 km

Q13. Priya is solving a Rule-of-Three problem where time is given in minutes for the first ratio and hours for the second. Which step must she take first?

• A. Multiply both ratios by 60 to balance them.
• B. Switch the position of distance and time in one ratio.
• C. Cross-multiply directly; units do not matter.
• D. Convert both time values to the same unit before setting up the proportion.

Q14. To share a quantity x in the ratio m : n, the chapter's method asks students to compute one quantity first. Which quantity is it?

• A. The product m × n.
• B. The HCF of m and n.
• C. The sum x + m + n.
• D. The size of each group, x / (m + n).

Q15. Asha and Bilal share 42 marbles in the ratio 4 : 3. Asha takes the larger share. How many marbles does each get?

• A. Asha 21, Bilal 21
• B. Asha 28, Bilal 14
• C. Asha 18, Bilal 24
• D. Asha 24, Bilal 18