Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 333 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.If 4 mangoes cost ₹56, how much do 6 mangoes cost? (a) ₹336 (b) ₹58 (c) ₹98 (d) ₹84
2. 2.If 2 pens cost ₹6, how much do 3 pens cost? (a) ₹18 (b) ₹7 (c) ₹12 (d) ₹9
3. 3.₹306 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹306 (b) ₹272 (c) ₹153 (d) ₹34
4. 4.If 7 mangoes cost ₹49, how much do 6 mangoes cost? (a) ₹294 (b) ₹49 (c) ₹48 (d) ₹42
5. 5.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 2 days (d) 11 days
6. 6.₹208 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹104 (b) ₹78 (c) ₹130 (d) ₹26
7. 7.If 8 kites cost ₹72, how much do 4 kites cost? (a) ₹68 (b) ₹36 (c) ₹288 (d) ₹45
8. 8.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 49 days (d) 9 days
9. 9.If 8 mangoes cost ₹24, how much do 4 mangoes cost? (a) ₹96 (b) ₹12 (c) ₹15 (d) ₹20
10. 10.₹532 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹190 (b) ₹38 (c) ₹266 (d) ₹342
11. 11.If 4 mangoes cost ₹32, how much do 2 mangoes cost? (a) ₹64 (b) ₹16 (c) ₹30 (d) ₹24
12. 12.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 22 days (d) 15 days
13. 13.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹200 (b) ₹50 (c) ₹275 (d) ₹350
14. 14.If 2 pens cost ₹20, how much do 5 pens cost? (a) ₹50 (b) ₹23 (c) ₹100 (d) ₹60
15. 15.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 1 day (d) 11 days
16. 16.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 27 days (c) 15 days (d) 28 days
17. 17.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 10 days (d) 12 days
18. 18.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 15 days (d) 20 days
19. 19.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹70 (b) ₹105 (c) ₹35 (d) ₹140
20. 20.₹552 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹276 (b) ₹230 (c) ₹46 (d) ₹322
21. 21.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹329 (b) ₹47 (c) ₹283 (d) ₹282
22. 22.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 7 days (d) 15 days
23. 23.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 9 days (d) 17 days
24. 24.If 2 mangoes cost ₹16, how much do 12 mangoes cost? (a) ₹96 (b) ₹192 (c) ₹104 (d) ₹26
25. 25.If 3 mangoes cost ₹33, how much do 4 mangoes cost? (a) ₹55 (b) ₹34 (c) ₹44 (d) ₹132
26. 26.If 3 mangoes cost ₹18, how much do 6 mangoes cost? (a) ₹36 (b) ₹42 (c) ₹108 (d) ₹21
27. 27.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 1 day (c) 15 days (d) 37 days
28. 28.₹90 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹18 (b) ₹45 (c) ₹36 (d) ₹54
29. 29.If 3 mangoes cost ₹9, how much do 12 mangoes cost? (a) ₹18 (b) ₹36 (c) ₹108 (d) ₹39
30. 30.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 10 days (d) 2 days
31. 31.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 13 days (d) 12 days
32. 32.₹330 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹99 (b) ₹231 (c) ₹33 (d) ₹165
33. 33.If 9 notebooks cost ₹153, how much do 5 notebooks cost? (a) ₹149 (b) ₹102 (c) ₹85 (d) ₹765
34. 34.If 8 notebooks cost ₹112, how much do 9 notebooks cost? (a) ₹113 (b) ₹140 (c) ₹126 (d) ₹1008
35. 35.If 7 pens cost ₹56, how much do 4 pens cost? (a) ₹40 (b) ₹224 (c) ₹53 (d) ₹32
36. 36.If 4 mangoes cost ₹28, how much do 10 mangoes cost? (a) ₹70 (b) ₹34 (c) ₹77 (d) ₹280
37. 37.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 9 days (d) 8 days
38. 38.₹494 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹152 (b) ₹38 (c) ₹342 (d) ₹247
39. 39.₹350 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹250 (b) ₹50 (c) ₹175 (d) ₹100
40. 40.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 3 days (d) 11 days

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