Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 969 · 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.₹384 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹192 (b) ₹240 (c) ₹48 (d) ₹144
2. 2.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 19 days (c) 18 days (d) 14 days
3. 3.₹90 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹70 (b) ₹20 (c) ₹45 (d) ₹10
4. 4.If 3 notebooks cost ₹48, how much do 12 notebooks cost? (a) ₹576 (b) ₹208 (c) ₹192 (d) ₹57
5. 5.₹145 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹58 (b) ₹116 (c) ₹29 (d) ₹87
6. 6.If 8 notebooks cost ₹56, how much do 12 notebooks cost? (a) ₹672 (b) ₹91 (c) ₹84 (d) ₹60
7. 7.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 9 days (d) 21 days
8. 8.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹210 (b) ₹42 (c) ₹252 (d) ₹231
9. 9.5 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 15 days (d) 11 days
10. 10.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 13 days (c) 12 days (d) 16 days
11. 11.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 6 days (d) 7 days
12. 12.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 11 days (d) 8 days
13. 13.If 6 pens cost ₹84, how much do 7 pens cost? (a) ₹85 (b) ₹98 (c) ₹112 (d) ₹588
14. 14.If 8 mangoes cost ₹96, how much do 4 mangoes cost? (a) ₹60 (b) ₹384 (c) ₹48 (d) ₹92
15. 15.If 2 pens cost ₹18, how much do 11 pens cost? (a) ₹99 (b) ₹27 (c) ₹108 (d) ₹198
16. 16.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 13 days (d) 12 days
17. 17.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 21 days (d) 11 days
18. 18.₹407 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹74 (b) ₹370 (c) ₹333 (d) ₹37
19. 19.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹40 (b) ₹8 (c) ₹32 (d) ₹24
20. 20.6 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 8 days (d) 3 days
21. 21.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹187 (b) ₹170 (c) ₹34 (d) ₹204
22. 22.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 22 days (d) 17 days
23. 23.₹60 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹25 (b) ₹5 (c) ₹30 (d) ₹35
24. 24.If 9 kites cost ₹117, how much do 8 kites cost? (a) ₹117 (b) ₹116 (c) ₹104 (d) ₹936
25. 25.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 1 day (d) 8 days
26. 26.If 3 kites cost ₹54, how much do 5 kites cost? (a) ₹56 (b) ₹270 (c) ₹108 (d) ₹90
27. 27.If 9 mangoes cost ₹99, how much do 12 mangoes cost? (a) ₹102 (b) ₹132 (c) ₹1188 (d) ₹143
28. 28.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹63 (b) ₹112 (c) ₹126 (d) ₹14
29. 29.₹301 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹258 (b) ₹43 (c) ₹86 (d) ₹215
30. 30.₹290 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹87 (b) ₹145 (c) ₹29 (d) ₹203
31. 31.₹517 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹235 (b) ₹282 (c) ₹47 (d) ₹329
32. 32.If 7 notebooks cost ₹161, how much do 5 notebooks cost? (a) ₹805 (b) ₹138 (c) ₹115 (d) ₹159
33. 33.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 5 days
34. 34.₹216 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹108 (b) ₹216 (c) ₹192 (d) ₹24
35. 35.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 26 days (d) 27 days
36. 36.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 5 days (d) 9 days
37. 37.₹207 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹115 (d) ₹138
38. 38.If 8 notebooks cost ₹176, how much do 10 notebooks cost? (a) ₹178 (b) ₹1760 (c) ₹220 (d) ₹242
39. 39.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 2 days (c) 32 days (d) 14 days
40. 40.If 4 pens cost ₹20, how much do 2 pens cost? (a) ₹10 (b) ₹18 (c) ₹15 (d) ₹40

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