Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 648 · 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.If 2 mangoes cost ₹26, how much do 3 mangoes cost? (a) ₹78 (b) ₹39 (c) ₹52 (d) ₹27
2. 2.If 5 notebooks cost ₹85, how much do 12 notebooks cost? (a) ₹204 (b) ₹1020 (c) ₹92 (d) ₹221
3. 3.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹91 (b) ₹70 (c) ₹112 (d) ₹14
4. 4.If 9 pens cost ₹63, how much do 10 pens cost? (a) ₹630 (b) ₹64 (c) ₹77 (d) ₹70
5. 5.₹414 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹184 (b) ₹230 (c) ₹46 (d) ₹207
6. 6.If 9 kites cost ₹108, how much do 10 kites cost? (a) ₹132 (b) ₹109 (c) ₹1080 (d) ₹120
7. 7.₹84 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹12 (b) ₹42 (c) ₹48 (d) ₹36
8. 8.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 9 days (d) 2 days
9. 9.If 6 notebooks cost ₹54, how much do 3 notebooks cost? (a) ₹51 (b) ₹36 (c) ₹27 (d) ₹162
10. 10.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 6 days (c) 18 days (d) 19 days
11. 11.If 7 mangoes cost ₹112, how much do 8 mangoes cost? (a) ₹896 (b) ₹113 (c) ₹144 (d) ₹128
12. 12.₹322 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹207 (b) ₹23 (c) ₹115 (d) ₹161
13. 13.₹172 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹43 (b) ₹86 (c) ₹129 (d) ₹172
14. 14.If 8 mangoes cost ₹128, how much do 4 mangoes cost? (a) ₹80 (b) ₹512 (c) ₹64 (d) ₹124
15. 15.₹360 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹360 (b) ₹45 (c) ₹315 (d) ₹180
16. 16.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 10 days (d) 4 days
17. 17.₹105 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹35 (b) ₹105 (c) ₹71 (d) ₹70
18. 18.If 7 notebooks cost ₹21, how much do 8 notebooks cost? (a) ₹22 (b) ₹168 (c) ₹27 (d) ₹24
19. 19.₹80 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹20 (b) ₹80 (c) ₹60 (d) ₹40
20. 20.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 18 days (c) 14 days (d) 19 days
21. 21.₹50 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹10 (b) ₹30 (c) ₹25 (d) ₹20
22. 22.₹156 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹12 (b) ₹108 (c) ₹78 (d) ₹48
23. 23.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹44 (b) ₹33 (c) ₹55 (d) ₹11
24. 24.If 7 pens cost ₹21, how much do 6 pens cost? (a) ₹21 (b) ₹20 (c) ₹18 (d) ₹126
25. 25.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 10 days (c) 5 days (d) 4 days
26. 26.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 36 days (c) 6 days (d) 4 days
27. 27.5 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
28. 28.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 4 days (d) 18 days
29. 29.7 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
30. 30.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 2 days (d) 4 days
31. 31.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 4 days (c) 25 days (d) 24 days
32. 32.₹462 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹252 (b) ₹42 (c) ₹210 (d) ₹231
33. 33.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 36 days (b) 11 days (c) 19 days (d) 35 days
34. 34.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 23 days (d) 22 days
35. 35.If 5 mangoes cost ₹125, how much do 3 mangoes cost? (a) ₹123 (b) ₹100 (c) ₹375 (d) ₹75
36. 36.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹13 (b) ₹78 (c) ₹91 (d) ₹65
37. 37.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹108 (b) ₹84 (c) ₹60 (d) ₹12
38. 38.₹280 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹175 (b) ₹140 (c) ₹105 (d) ₹35
39. 39.If 4 notebooks cost ₹20, how much do 12 notebooks cost? (a) ₹28 (b) ₹60 (c) ₹240 (d) ₹65
40. 40.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹55 (b) ₹10 (c) ₹40 (d) ₹70

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