Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 934 · 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.₹312 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹195 (b) ₹156 (c) ₹117 (d) ₹39
2. 2.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 6 days (d) 9 days
3. 3.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹102 (b) ₹136 (c) ₹119 (d) ₹34
4. 4.If 6 notebooks cost ₹108, how much do 4 notebooks cost? (a) ₹432 (b) ₹106 (c) ₹72 (d) ₹90
5. 5.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 8 days (d) 9 days
6. 6.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹135 (b) ₹120 (c) ₹30 (d) ₹150
7. 7.₹286 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹143 (b) ₹234 (c) ₹52 (d) ₹26
8. 8.If 6 notebooks cost ₹138, how much do 12 notebooks cost? (a) ₹276 (b) ₹144 (c) ₹1656 (d) ₹299
9. 9.₹264 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹96 (b) ₹168 (c) ₹132 (d) ₹24
10. 10.If 5 notebooks cost ₹85, how much do 3 notebooks cost? (a) ₹255 (b) ₹51 (c) ₹83 (d) ₹68
11. 11.₹462 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹231 (b) ₹42 (c) ₹294 (d) ₹168
12. 12.If 6 kites cost ₹60, how much do 9 kites cost? (a) ₹540 (b) ₹100 (c) ₹90 (d) ₹63
13. 13.If 9 notebooks cost ₹225, how much do 7 notebooks cost? (a) ₹200 (b) ₹223 (c) ₹1575 (d) ₹175
14. 14.If 9 pens cost ₹108, how much do 10 pens cost? (a) ₹132 (b) ₹120 (c) ₹109 (d) ₹1080
15. 15.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 11 days (c) 1 day (d) 2 days
16. 16.₹377 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹261 (b) ₹232 (c) ₹145 (d) ₹29
17. 17.7 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 8 days (d) 6 days
18. 18.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 11 days (d) 3 days
19. 19.₹203 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹58 (b) ₹29 (c) ₹145 (d) ₹174
20. 20.If 4 mangoes cost ₹80, how much do 12 mangoes cost? (a) ₹260 (b) ₹960 (c) ₹88 (d) ₹240
21. 21.₹112 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹112 (b) ₹28 (c) ₹84 (d) ₹56
22. 22.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 10 days (d) 17 days
23. 23.₹338 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹234 (b) ₹169 (c) ₹26 (d) ₹104
24. 24.If 3 pens cost ₹54, how much do 9 pens cost? (a) ₹180 (b) ₹162 (c) ₹486 (d) ₹60
25. 25.6 workers can build a wall in 10 days. How many days will 4 workers take, working at the same speed? (a) 12 days (b) 15 days (c) 8 days (d) 16 days
26. 26.If 2 kites cost ₹14, how much do 3 kites cost? (a) ₹15 (b) ₹42 (c) ₹28 (d) ₹21
27. 27.If 4 pens cost ₹92, how much do 10 pens cost? (a) ₹98 (b) ₹920 (c) ₹230 (d) ₹253
28. 28.If 8 notebooks cost ₹112, how much do 12 notebooks cost? (a) ₹1344 (b) ₹168 (c) ₹182 (d) ₹116
29. 29.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 21 days (d) 22 days
30. 30.If 9 notebooks cost ₹45, how much do 3 notebooks cost? (a) ₹135 (b) ₹39 (c) ₹20 (d) ₹15
31. 31.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 7 days (d) 3 days
32. 32.6 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 2 days (d) 7 days
33. 33.₹470 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹235 (b) ₹47 (c) ₹329 (d) ₹141
34. 34.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 7 days (d) 8 days
35. 35.If 2 pens cost ₹40, how much do 10 pens cost? (a) ₹220 (b) ₹48 (c) ₹400 (d) ₹200
36. 36.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 8 days (d) 2 days
37. 37.₹78 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹78 (b) ₹13 (c) ₹65 (d) ₹39
38. 38.If 2 kites cost ₹28, how much do 10 kites cost? (a) ₹36 (b) ₹140 (c) ₹154 (d) ₹280
39. 39.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 5 days (d) 45 days
40. 40.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 11 days (d) 14 days

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