Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 903 · 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.₹484 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹88 (b) ₹242 (c) ₹44 (d) ₹396
2. 2.If 4 notebooks cost ₹28, how much do 5 notebooks cost? (a) ₹42 (b) ₹35 (c) ₹140 (d) ₹29
3. 3.If 7 mangoes cost ₹77, how much do 8 mangoes cost? (a) ₹78 (b) ₹88 (c) ₹99 (d) ₹616
4. 4.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 39 days (b) 9 days (c) 40 days (d) 17 days
5. 5.If 4 notebooks cost ₹76, how much do 6 notebooks cost? (a) ₹78 (b) ₹114 (c) ₹456 (d) ₹133
6. 6.If 2 mangoes cost ₹46, how much do 9 mangoes cost? (a) ₹207 (b) ₹414 (c) ₹230 (d) ₹53
7. 7.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 6 days (d) 7 days
8. 8.₹49 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹35 (b) ₹14 (c) ₹42 (d) ₹7
9. 9.If 3 notebooks cost ₹33, how much do 2 notebooks cost? (a) ₹32 (b) ₹22 (c) ₹33 (d) ₹66
10. 10.₹148 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹111 (b) ₹148 (c) ₹74 (d) ₹37
11. 11.₹63 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹28 (b) ₹42 (c) ₹35 (d) ₹7
12. 12.If 9 mangoes cost ₹162, how much do 6 mangoes cost? (a) ₹126 (b) ₹972 (c) ₹108 (d) ₹159
13. 13.If 3 notebooks cost ₹9, how much do 5 notebooks cost? (a) ₹18 (b) ₹45 (c) ₹15 (d) ₹11
14. 14.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 7 days (c) 8 days (d) 2 days
15. 15.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 1 day (d) 10 days
16. 16.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 6 days (d) 18 days
17. 17.If 6 pens cost ₹132, how much do 3 pens cost? (a) ₹66 (b) ₹396 (c) ₹129 (d) ₹88
18. 18.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 10 days
19. 19.If 8 notebooks cost ₹112, how much do 4 notebooks cost? (a) ₹108 (b) ₹70 (c) ₹56 (d) ₹448
20. 20.₹385 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹35 (b) ₹70 (c) ₹350 (d) ₹315
21. 21.₹540 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹270 (b) ₹225 (c) ₹45 (d) ₹315
22. 22.₹111 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹75 (b) ₹37 (c) ₹74 (d) ₹111
23. 23.If 8 mangoes cost ₹48, how much do 2 mangoes cost? (a) ₹42 (b) ₹96 (c) ₹18 (d) ₹12
24. 24.₹45 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹20 (c) ₹25 (d) ₹5
25. 25.If 3 mangoes cost ₹48, how much do 4 mangoes cost? (a) ₹192 (b) ₹64 (c) ₹80 (d) ₹49
26. 26.If 2 pens cost ₹32, how much do 7 pens cost? (a) ₹112 (b) ₹128 (c) ₹37 (d) ₹224
27. 27.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 13 days (b) 16 days (c) 2 days (d) 1 day
28. 28.If 2 kites cost ₹24, how much do 3 kites cost? (a) ₹48 (b) ₹72 (c) ₹36 (d) ₹25
29. 29.₹110 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹60 (b) ₹50 (c) ₹55 (d) ₹10
30. 30.If 8 pens cost ₹40, how much do 11 pens cost? (a) ₹43 (b) ₹55 (c) ₹60 (d) ₹440
31. 31.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 45 days (d) 5 days
32. 32.If 2 kites cost ₹40, how much do 4 kites cost? (a) ₹42 (b) ₹160 (c) ₹100 (d) ₹80
33. 33.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 5 days (d) 7 days
34. 34.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹66 (b) ₹22 (c) ₹55 (d) ₹44
35. 35.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 12 days (d) 17 days
36. 36.₹144 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹64 (b) ₹80 (c) ₹72 (d) ₹16
37. 37.₹378 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹189 (b) ₹210 (c) ₹42 (d) ₹168
38. 38.₹252 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹18 (b) ₹126 (c) ₹162 (d) ₹90
39. 39.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 1 day (c) 22 days (d) 21 days
40. 40.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 25 days (d) 13 days

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