Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 774 · 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.₹24 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹24 (b) ₹12 (c) ₹18 (d) ₹6
2. 2.If 6 pens cost ₹108, how much do 11 pens cost? (a) ₹198 (b) ₹1188 (c) ₹216 (d) ₹113
3. 3.₹132 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹12 (b) ₹84 (c) ₹66 (d) ₹48
4. 4.If 2 mangoes cost ₹40, how much do 3 mangoes cost? (a) ₹80 (b) ₹60 (c) ₹41 (d) ₹120
5. 5.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 6 days
6. 6.If 6 mangoes cost ₹84, how much do 3 mangoes cost? (a) ₹42 (b) ₹81 (c) ₹56 (d) ₹252
7. 7.If 6 notebooks cost ₹30, how much do 12 notebooks cost? (a) ₹360 (b) ₹65 (c) ₹60 (d) ₹36
8. 8.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 21 days (d) 22 days
9. 9.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 20 days (b) 14 days (c) 6 days (d) 5 days
10. 10.If 9 mangoes cost ₹135, how much do 7 mangoes cost? (a) ₹945 (b) ₹105 (c) ₹133 (d) ₹120
11. 11.9 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 6 days (d) 7 days
12. 12.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 18 days (c) 7 days (d) 10 days
13. 13.If 2 pens cost ₹8, how much do 3 pens cost? (a) ₹24 (b) ₹12 (c) ₹16 (d) ₹9
14. 14.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 11 days
15. 15.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 16 days (d) 5 days
16. 16.If 8 notebooks cost ₹152, how much do 3 notebooks cost? (a) ₹76 (b) ₹57 (c) ₹456 (d) ₹147
17. 17.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 15 days (c) 23 days (d) 22 days
18. 18.₹96 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹40 (d) ₹48
19. 19.If 9 mangoes cost ₹198, how much do 5 mangoes cost? (a) ₹990 (b) ₹110 (c) ₹194 (d) ₹132
20. 20.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 11 days (d) 5 days
21. 21.₹288 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹144 (b) ₹128 (c) ₹160 (d) ₹32
22. 22.₹470 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹235 (b) ₹470 (c) ₹47 (d) ₹423
23. 23.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 8 days (d) 10 days
24. 24.₹216 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹120 (b) ₹24 (c) ₹96 (d) ₹108
25. 25.₹322 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹184 (b) ₹46 (c) ₹161 (d) ₹138
26. 26.₹120 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹15 (b) ₹60 (c) ₹75 (d) ₹45
27. 27.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹75 (b) ₹15 (c) ₹105 (d) ₹90
28. 28.₹72 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹36 (b) ₹72 (c) ₹24 (d) ₹48
29. 29.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 5 days (d) 6 days
30. 30.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 8 days (d) 14 days
31. 31.6 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 15 days (b) 18 days (c) 8 days (d) 9 days
32. 32.If 8 notebooks cost ₹64, how much do 7 notebooks cost? (a) ₹56 (b) ₹64 (c) ₹63 (d) ₹448
33. 33.If 6 pens cost ₹42, how much do 2 pens cost? (a) ₹14 (b) ₹38 (c) ₹84 (d) ₹21
34. 34.If 4 pens cost ₹16, how much do 9 pens cost? (a) ₹36 (b) ₹21 (c) ₹144 (d) ₹40
35. 35.₹322 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹92 (b) ₹161 (c) ₹46 (d) ₹230
36. 36.₹462 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹33 (b) ₹297 (c) ₹165 (d) ₹231
37. 37.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 4 days (d) 18 days
38. 38.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 3 days (d) 7 days
39. 39.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 12 days (c) 16 days (d) 13 days
40. 40.₹70 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹70 (b) ₹63 (c) ₹7 (d) ₹35

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