Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 140 · 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.₹299 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹184 (d) ₹207
2. 2.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹25 (b) ₹175 (c) ₹150 (d) ₹125
3. 3.If 4 mangoes cost ₹44, how much do 2 mangoes cost? (a) ₹42 (b) ₹22 (c) ₹33 (d) ₹88
4. 4.₹364 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹224 (d) ₹182
5. 5.If 7 kites cost ₹98, how much do 10 kites cost? (a) ₹980 (b) ₹154 (c) ₹101 (d) ₹140
6. 6.If 8 mangoes cost ₹32, how much do 7 mangoes cost? (a) ₹224 (b) ₹32 (c) ₹31 (d) ₹28
7. 7.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 27 days (c) 26 days (d) 28 days
8. 8.7 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 17 days (b) 8 days (c) 7 days (d) 6 days
9. 9.If 5 notebooks cost ₹95, how much do 12 notebooks cost? (a) ₹1140 (b) ₹247 (c) ₹102 (d) ₹228
10. 10.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 1 day (d) 17 days
11. 11.If 2 kites cost ₹16, how much do 7 kites cost? (a) ₹56 (b) ₹112 (c) ₹21 (d) ₹64
12. 12.If 7 kites cost ₹168, how much do 4 kites cost? (a) ₹672 (b) ₹96 (c) ₹120 (d) ₹165
13. 13.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 25 days (c) 13 days (d) 9 days
14. 14.₹243 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹54 (b) ₹189 (c) ₹27 (d) ₹216
15. 15.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹119 (b) ₹102 (c) ₹34 (d) ₹136
16. 16.If 3 notebooks cost ₹75, how much do 9 notebooks cost? (a) ₹81 (b) ₹675 (c) ₹225 (d) ₹250
17. 17.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹63 (b) ₹9 (c) ₹27 (d) ₹45
18. 18.If 9 mangoes cost ₹198, how much do 5 mangoes cost? (a) ₹110 (b) ₹990 (c) ₹132 (d) ₹194
19. 19.₹344 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹215 (b) ₹129 (c) ₹172 (d) ₹43
20. 20.If 2 notebooks cost ₹46, how much do 12 notebooks cost? (a) ₹299 (b) ₹552 (c) ₹56 (d) ₹276
21. 21.If 2 pens cost ₹30, how much do 5 pens cost? (a) ₹90 (b) ₹150 (c) ₹33 (d) ₹75
22. 22.If 9 pens cost ₹207, how much do 12 pens cost? (a) ₹2484 (b) ₹276 (c) ₹299 (d) ₹210
23. 23.If 3 kites cost ₹66, how much do 5 kites cost? (a) ₹68 (b) ₹132 (c) ₹110 (d) ₹330
24. 24.If 2 mangoes cost ₹14, how much do 6 mangoes cost? (a) ₹18 (b) ₹42 (c) ₹84 (d) ₹49
25. 25.If 8 notebooks cost ₹24, how much do 2 notebooks cost? (a) ₹9 (b) ₹18 (c) ₹6 (d) ₹48
26. 26.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 3 days (b) 28 days (c) 27 days (d) 15 days
27. 27.If 7 pens cost ₹91, how much do 2 pens cost? (a) ₹26 (b) ₹86 (c) ₹39 (d) ₹182
28. 28.₹324 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹324 (b) ₹288 (c) ₹162 (d) ₹36
29. 29.₹374 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹68 (b) ₹306 (c) ₹34 (d) ₹187
30. 30.If 4 kites cost ₹88, how much do 6 kites cost? (a) ₹528 (b) ₹90 (c) ₹132 (d) ₹154
31. 31.₹256 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹32 (b) ₹128 (c) ₹256 (d) ₹224
32. 32.₹132 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹66 (b) ₹88 (c) ₹132 (d) ₹44
33. 33.8 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 14 days (d) 20 days
34. 34.₹147 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹63 (b) ₹84 (c) ₹105 (d) ₹21
35. 35.4 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 9 days (d) 4 days
36. 36.₹220 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹160 (b) ₹110 (c) ₹60 (d) ₹20
37. 37.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 35 days (b) 17 days (c) 36 days (d) 11 days
38. 38.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 7 days (d) 20 days
39. 39.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 8 days (d) 6 days
40. 40.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 3 days (d) 2 days

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