Ratios Percentages and Commercial Comparisons Module Review

How to use this review

Attempt this review after the four Ratios Percentages and Commercial Comparisons lessons. Each of the 20 independent questions has exactly one correct option and is worth one mark. This original learning review is free and untimed: +1 for correct, 0 for incorrect or unattempted, no negative marking and no pass cutoff. Five questions per lesson are a coverage choice, not predicted RRB exam weighting. This is not a full CBT simulation. Write a named base, invariant or short calculation before reading the answer key. Unless a question says otherwise, price comparisons use the stated positive total cost as the profit/loss base and marked price as the discount base. Read every fixed-rate and unit condition in the individual question.

Questions

1. What is 150 g:0.6 kg in simplest form, in this order?

A. 4:1 B. 1:4 C. 1:400 D. 250:1

2. What percentage is exactly equal to 7/20?

A. 0.35% B. 3.5% C. 35% D. 350%

3. An item costs ₹560 and sells for ₹630, with no other costs. What is the cost-based profit percentage?

A. 12.5% B. 11 1/9% C. 70% D. 112.5%

4. At one fixed unit price with no extra fees, 7 identical items cost ₹189. What do 11 items cost?

A. ₹27 B. ₹193 C. ₹189 D. ₹297

5. An item is marked ₹1,400. A 9% discount on marked price is applied, with no additional charge. Find its selling price.

A. ₹126 B. ₹1,391 C. ₹1,274 D. ₹1,526

6. What is 16% of 375?

A. 6 B. 16 C. 6000 D. 60

7. Find x in 8:13=40:x.

A. 65 B. 45 C. 32 D. 40

8. Positive x and y are inversely proportional. When x=8, y=15. Find y when x=12.

A. 22.5 B. 10 C. 120 D. 19

9. A total of 990 is divided into three shares in the ratio 2:4:5. What is the share corresponding to 4?

A. 90 B. 450 C. 360 D. 180

10. At a constant flow rate, 45 L flows in 6 minutes. How much flows in 14 minutes, with no interruption?

A. 105 L B. 53 L C. 7.5 L D. 630 L

11. A positive value is 378 after a 10% decrease. What was its original value?

A. 415.8 B. 420 C. 340.2 D. 388

12. An item is purchased for ₹1,250 and transport of ₹150 is explicitly included in its cost. It sells for ₹1,610, with no other costs. Find profit as a percentage of total cost.

A. 28.8% B. 13 1/23% C. 210% D. 15%

13. A fixed stock feeds 28 people for 18 days. Each person consumes the same daily amount, unchanged in both cases. With no wastage, how long would this stock feed 42 people?

A. 27 days B. 504 days C. 14 days D. 12 days

14. A positive quantity rises 15%, then falls 20% of the new value. What is the net change relative to the original?

A. 5% decrease B. 8% increase C. 8% decrease D. 35% decrease

15. Two positive lengths are in the ratio 3:8 and differ by 75 cm. What is their sum?

A. 45 cm B. 165 cm C. 120 cm D. 75 cm

16. An item costs ₹900. Its marked price is set 40% above cost, then a 15% discount on marked price is given. With no other costs, what is the cost-based profit percentage?

A. 19% B. 25% C. 55% D. 15%

17. The corresponding pairs are (x,y)=(1,8),(2,11),(4,17). Which statement about these supplied pairs is correct?

A. They satisfy direct proportion because both values increase B. They satisfy neither direct nor inverse proportion C. They satisfy inverse proportion because x and y differ D. They satisfy both direct and inverse proportion

18. Two items cost ₹200 and ₹800. The first sells at 25% profit on its cost and the second at 5% loss on its cost. Both are sold, with no other costs. What is the overall result as a percentage of total cost?

A. 1% profit B. 10% profit C. 20% profit D. 1% loss

19. A rate changes from 25% to 35%. Which pair gives the percentage-point increase and relative percentage increase, in that order?

A. 10 percentage points; 10% B. 40 percentage points; 10% C. 10 percentage points; 140% D. 10 percentage points; 40%

20. Let A, B and C be positive quantities with A:B=5:6 and B:C=9:4. What is A:B:C?

A. 5:6:4 B. 15:9:4 C. 15:18:8 D. 5:18:4

Explained answer key

1. B. 0.6 kg=600 g, so 150:600=1:4. Check 150/600=0.25. A reverses the order. C introduces an extra factor of 100 into the second term. D divides 150 by 0.6 without matching grams and kilograms.

2. C. 7/20×100=35, so 7/20=35%. Check 35/100=7/20. A writes the decimal 0.35 with an extra percent sign, reducing its value by 100. B and D shift the decimal one place too little or too far relative to the correct percentage.

3. A. Profit=₹630−₹560=₹70. The required base is cost ₹560: 70/560×100=12.5%. Check 560×1.125=630. B uses selling price as denominator, giving a sales-based margin instead. C confuses rupees of profit with its percentage. D is SP as a percentage of cost, not the profit percentage.

4. D. One item costs ₹189÷7=₹27. Eleven cost 11×₹27=₹297. Check that cost/item stays ₹27. A gives only one item. B adds the count increase 4 to the monetary total. C keeps the old total although more items are bought at a positive fixed rate.

5. C. Discount=0.09×₹1,400=₹126. Selling price=₹1,400−₹126=₹1,274, or ₹1,400×0.91. A gives only the discount; B subtracts ₹9 instead of 9%; D adds the discount. Check ₹1,274+₹126=₹1,400.

6. D. 16% of 375=(16/100)×375=60. Check 60/375=0.16. A is ten times too small. B repeats the numerical percentage rather than finding an amount. C multiplies by 16 without dividing by 100.

7. A. The first term was multiplied by 5: 8×5=40. Apply the same factor to 13: x=65. Check 8×65=13×40=520. B adds 32 to 13; C gives the additive change in the first term; D repeats 40 and would make the second ratio 1:1.

8. B. The fixed product is xy=8×15=120. Therefore y=120÷12=10. Check 12×10=120. A applies the direct factor 12/8 instead of the inverse factor 8/12. C gives the invariant product, not y. D adds 4 to y because 4 was added to x.

9. C. There are 2+4+5=11 equal parts, each 990÷11=90. The requested share is 4×90=360. The other shares are 180 and 450; together they total 990. A gives one part, B the five-part share and D the two-part share.

10. A. Rate=45÷6=7.5 L/min. In 14 minutes, volume=7.5×14=105 L. Check 105/14=45/6. B adds the time increase 8 to the volume. C gives the amount for only one minute. D multiplies 45 by 14 without first accounting for the given 6 minutes.

11. B. The final 378 is 90% of the original. Original=378÷0.90=420. Check 420−42=378. A adds 10% of the final, using the wrong base. C decreases the final again. D adds the number 10 rather than reversing the factor 0.9.

12. D. Total cost=₹1,250+₹150=₹1,400. Profit=₹1,610−₹1,400=₹210. Percentage=210/1400×100=15%. Check 1400×1.15=1610. A omits transport and uses (1610−1250)/1250. B uses sales ₹1,610 as denominator: 21000/1610=300/23%=13 1/23%. C mistakes the profit amount for its percentage.

13. D. The fixed stock supports 28×18=504 person-days under the stated consumption rate. For 42 people, duration=504÷42=12 days. Check 42×12=504. A uses direct rather than inverse scaling. B gives person-days but labels them days. C repeats the increase in people, which does not directly determine days.

14. C. The factor is 1.15×0.80=0.92. Thus 92% remains, a decrease of 8%. Starting from 100 gives 100→115→92. A subtracts the two percentage numbers without tracking the new base. B reverses the direction. D adds the magnitudes of both changes as though both were decreases of the original.

15. B. The difference represents 8−3=5 equal parts. One part=75÷5=15 cm. The sum is (3+8)×15=165 cm. Check lengths 45 cm and 120 cm differ by 75 cm. A and C give the individual lengths. D repeats the difference rather than finding the sum.

16. A. Marked price=900×1.40=₹1,260. SP=1260×0.85=₹1,071. Profit=₹171, so 171/900×100=19%. Equivalently, 1.40×0.85=1.19. B subtracts unlike-base rates 40−15. C adds them despite the discount. D repeats the discount rate, which has a different base and purpose.

17. B. For direct proportion, y/x would be constant, but the quotients are 8, 11/2 and 17/4. For inverse proportion, xy would be constant, but the products are 8, 22 and 68. Neither test passes. A uses direction alone. C uses unequal values, which is not an inverse-proportion test. D contradicts both failed checks. We judge the supplied pairs, not infer an unspecified law beyond them.

18. A. First receipt=200×1.25=₹250. Second receipt=800×0.95=₹760. Total receipt=₹1,010 against total cost ₹1,000, giving ₹10 profit and 1%. B averages +25% and −5% despite unequal cost bases. C merely subtracts 5 from 25. D reverses the sign even though receipts exceed cost.

19. D. The numerical rate difference is 35−25=10 percentage points. Relative increase=(10/25)×100=40%. Check 25×1.4=35. A equates points with relative percent. B swaps quantities and labels. C gives the final rate as 140% of the old rate, not its 40% increase.

20. C. Match B at 18. Scale 5:6 by 3 to get 15:18, and scale 9:4 by 2 to get 18:8. Thus A:B:C=15:18:8. Check 15:18=5:6 and 18:8=9:4. A joins unmatched terms; B preserves B:C=9:4, but 15:9 is not 5:6: A and B were scaled inconsistently. D changes B without preserving either adjoining ratio.

Learn from the errors

• Wrong ratio or unit? Revisit Ratio and Proportion; label each term and match units first
• Wrong relationship? Revisit Direct and Inverse Proportion; test the quotient or product and state what is fixed
• Wrong percentage? Revisit Percentages and Successive Changes; circle the 100% base at every stage
• Wrong price comparison? Revisit Profit Loss and Discount; distinguish total cost, marked price and selling price

A score is feedback, not a readiness guarantee. For every missed question, explain why the keyed option satisfies the conditions and why your choice does not. Then retry without looking at the solution.

Sources and originality

The scope follows RRB CEN 09/2025 §14.1, printed p.28: Ratio and Proportion, Percentages, and Profit and Loss. Original review questions assess our four lessons and are distinct from their lesson-practice questions. Mathematical references: NCERT Proportional Reasoning–1, §§7.1–7.6, printed pp.159–177; Proportional Reasoning–2, §§3.1–3.4 and §3.6, pp.55–60 and 63–67; Direct and Inverse Proportions, 2024–25 reprint, §§11.2–11.3, pp.129–143; Fractions in Disguise, §§1.1–1.3, relevant pp.1–19 and 26–27; NIOS Chapter 8, §§8.1–8.5.2, pp.204–219; Hindi counterpart, pp.212–229. No textbook question or scan is reproduced. Percentage points are a bounded teaching extension, not a separately named RRB topic.

Quick reference

Review routine: name the comparison → match units → identify the base or fixed relationship → calculate exactly → verify in the original conditions. For price chains, write cost → marked price → selling price. Revisit the full lesson quick references before a second attempt, rather than use a numerical pass threshold.