Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 638 · 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.₹630 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹45 (b) ₹405 (c) ₹225 (d) ₹315
2. 2.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 8 days (d) 3 days
3. 3.If 3 kites cost ₹51, how much do 7 kites cost? (a) ₹136 (b) ₹55 (c) ₹357 (d) ₹119
4. 4.If 5 mangoes cost ₹105, how much do 2 mangoes cost? (a) ₹42 (b) ₹102 (c) ₹63 (d) ₹210
5. 5.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹160 (b) ₹208 (c) ₹32 (d) ₹256
6. 6.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹6 (b) ₹33 (c) ₹30 (d) ₹36
7. 7.If 8 notebooks cost ₹32, how much do 2 notebooks cost? (a) ₹8 (b) ₹64 (c) ₹12 (d) ₹26
8. 8.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹42 (b) ₹70 (c) ₹14 (d) ₹98
9. 9.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 3 days (b) 7 days (c) 6 days (d) 8 days
10. 10.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 3 days (d) 8 days
11. 11.If 2 notebooks cost ₹38, how much do 4 notebooks cost? (a) ₹95 (b) ₹40 (c) ₹152 (d) ₹76
12. 12.₹455 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹35 (b) ₹315 (c) ₹175 (d) ₹280
13. 13.If 3 mangoes cost ₹24, how much do 4 mangoes cost? (a) ₹40 (b) ₹32 (c) ₹96 (d) ₹25
14. 14.3 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
15. 15.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 13 days (d) 11 days
16. 16.If 5 pens cost ₹40, how much do 2 pens cost? (a) ₹80 (b) ₹37 (c) ₹24 (d) ₹16
17. 17.₹105 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹105 (c) ₹90 (d) ₹15
18. 18.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 11 days (d) 8 days
19. 19.If 9 kites cost ₹54, how much do 10 kites cost? (a) ₹55 (b) ₹540 (c) ₹60 (d) ₹66
20. 20.If 8 mangoes cost ₹64, how much do 10 mangoes cost? (a) ₹88 (b) ₹640 (c) ₹80 (d) ₹66
21. 21.If 9 pens cost ₹54, how much do 5 pens cost? (a) ₹36 (b) ₹270 (c) ₹50 (d) ₹30
22. 22.If 7 mangoes cost ₹42, how much do 8 mangoes cost? (a) ₹336 (b) ₹48 (c) ₹54 (d) ₹43
23. 23.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 29 days (b) 13 days (c) 1 day (d) 28 days
24. 24.If 9 mangoes cost ₹216, how much do 5 mangoes cost? (a) ₹120 (b) ₹212 (c) ₹1080 (d) ₹144
25. 25.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 13 days (d) 16 days
26. 26.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹220 (b) ₹352 (c) ₹286 (d) ₹44
27. 27.If 2 pens cost ₹46, how much do 8 pens cost? (a) ₹207 (b) ₹52 (c) ₹368 (d) ₹184
28. 28.If 4 notebooks cost ₹64, how much do 10 notebooks cost? (a) ₹640 (b) ₹176 (c) ₹70 (d) ₹160
29. 29.If 9 mangoes cost ₹198, how much do 10 mangoes cost? (a) ₹199 (b) ₹1980 (c) ₹242 (d) ₹220
30. 30.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 4 days (d) 5 days
31. 31.If 6 pens cost ₹18, how much do 2 pens cost? (a) ₹36 (b) ₹14 (c) ₹6 (d) ₹9
32. 32.₹176 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹16 (b) ₹144 (c) ₹32 (d) ₹88
33. 33.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 15 days (d) 9 days
34. 34.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹24 (b) ₹108 (c) ₹66 (d) ₹12
35. 35.If 5 kites cost ₹15, how much do 7 kites cost? (a) ₹105 (b) ₹24 (c) ₹17 (d) ₹21
36. 36.If 4 pens cost ₹56, how much do 12 pens cost? (a) ₹64 (b) ₹672 (c) ₹182 (d) ₹168
37. 37.₹308 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹224 (b) ₹84 (c) ₹154 (d) ₹28
38. 38.6 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 4 days (d) 2 days
39. 39.4 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 31 days (c) 17 days (d) 30 days
40. 40.If 5 pens cost ₹65, how much do 8 pens cost? (a) ₹117 (b) ₹520 (c) ₹104 (d) ₹68

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