Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 128 · 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.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹126 (b) ₹162 (c) ₹18 (d) ₹90
2. 2.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 4 days (d) 6 days
3. 3.₹407 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹37 (b) ₹296 (c) ₹333 (d) ₹111
4. 4.If 3 kites cost ₹21, how much do 5 kites cost? (a) ₹35 (b) ₹23 (c) ₹105 (d) ₹42
5. 5.₹294 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹42 (b) ₹252 (c) ₹147 (d) ₹294
6. 6.If 6 pens cost ₹138, how much do 7 pens cost? (a) ₹139 (b) ₹184 (c) ₹966 (d) ₹161
7. 7.If 4 pens cost ₹16, how much do 7 pens cost? (a) ₹19 (b) ₹32 (c) ₹112 (d) ₹28
8. 8.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 11 days (c) 7 days (d) 17 days
9. 9.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 4 days (d) 6 days
10. 10.₹252 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹126 (d) ₹112
11. 11.₹56 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹49 (b) ₹56 (c) ₹28 (d) ₹7
12. 12.₹384 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹192 (b) ₹160 (c) ₹224 (d) ₹32
13. 13.If 7 pens cost ₹112, how much do 6 pens cost? (a) ₹96 (b) ₹112 (c) ₹111 (d) ₹672
14. 14.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 11 days (d) 5 days
15. 15.₹225 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹200 (b) ₹201 (c) ₹225 (d) ₹25
16. 16.₹170 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹119 (b) ₹85 (c) ₹17 (d) ₹51
17. 17.₹170 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹68 (b) ₹85 (c) ₹102 (d) ₹34
18. 18.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 4 days (d) 1 day
19. 19.9 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 12 days (c) 10 days (d) 13 days
20. 20.If 8 kites cost ₹24, how much do 12 kites cost? (a) ₹36 (b) ₹288 (c) ₹39 (d) ₹28
21. 21.₹121 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹88 (b) ₹99 (c) ₹11 (d) ₹33
22. 22.If 4 notebooks cost ₹48, how much do 11 notebooks cost? (a) ₹55 (b) ₹132 (c) ₹144 (d) ₹528
23. 23.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 2 days (d) 1 day
24. 24.If 5 notebooks cost ₹55, how much do 2 notebooks cost? (a) ₹22 (b) ₹52 (c) ₹110 (d) ₹33
25. 25.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 10 days (c) 28 days (d) 18 days
26. 26.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 13 days (c) 5 days (d) 7 days
27. 27.₹110 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹33 (b) ₹55 (c) ₹11 (d) ₹77
28. 28.If 5 mangoes cost ₹115, how much do 9 mangoes cost? (a) ₹207 (b) ₹1035 (c) ₹230 (d) ₹119
29. 29.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 7 days
30. 30.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹49 (b) ₹343 (c) ₹245 (d) ₹294
31. 31.₹238 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹119 (b) ₹85 (c) ₹17 (d) ₹153
32. 32.If 2 mangoes cost ₹36, how much do 6 mangoes cost? (a) ₹40 (b) ₹126 (c) ₹216 (d) ₹108
33. 33.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 11 days (d) 4 days
34. 34.If 9 pens cost ₹81, how much do 2 pens cost? (a) ₹74 (b) ₹162 (c) ₹27 (d) ₹18
35. 35.4 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 4 days (d) 3 days
36. 36.₹387 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹86 (b) ₹43 (c) ₹301 (d) ₹344
37. 37.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 8 days (d) 12 days
38. 38.₹539 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹392 (b) ₹147 (c) ₹441 (d) ₹49
39. 39.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 7 days (d) 25 days
40. 40.If 9 pens cost ₹207, how much do 12 pens cost? (a) ₹2484 (b) ₹210 (c) ₹276 (d) ₹299

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