Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 466 · 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.₹492 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹41 (b) ₹246 (c) ₹287 (d) ₹205
2. 2.6 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 11 days (d) 12 days
3. 3.₹490 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹245 (b) ₹315 (c) ₹35 (d) ₹175
4. 4.If 3 mangoes cost ₹66, how much do 7 mangoes cost? (a) ₹154 (b) ₹176 (c) ₹462 (d) ₹70
5. 5.₹124 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹31 (b) ₹93 (c) ₹124 (d) ₹62
6. 6.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹63 (b) ₹14 (c) ₹126 (d) ₹112
7. 7.6 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 19 days (c) 10 days (d) 18 days
8. 8.₹70 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹28 (b) ₹14 (c) ₹35 (d) ₹42
9. 9.If 3 kites cost ₹60, how much do 7 kites cost? (a) ₹420 (b) ₹64 (c) ₹140 (d) ₹160
10. 10.If 6 notebooks cost ₹96, how much do 5 notebooks cost? (a) ₹480 (b) ₹95 (c) ₹80 (d) ₹96
11. 11.If 6 pens cost ₹78, how much do 4 pens cost? (a) ₹312 (b) ₹52 (c) ₹76 (d) ₹65
12. 12.₹528 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹264 (b) ₹48 (c) ₹336 (d) ₹192
13. 13.If 4 pens cost ₹72, how much do 5 pens cost? (a) ₹90 (b) ₹73 (c) ₹108 (d) ₹360
14. 14.If 8 mangoes cost ₹184, how much do 12 mangoes cost? (a) ₹188 (b) ₹299 (c) ₹276 (d) ₹2208
15. 15.If 3 pens cost ₹24, how much do 4 pens cost? (a) ₹96 (b) ₹32 (c) ₹40 (d) ₹25
16. 16.₹400 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹120 (b) ₹40 (c) ₹280 (d) ₹200
17. 17.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹43 (b) ₹215 (c) ₹301 (d) ₹258
18. 18.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 19 days (d) 11 days
19. 19.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 9 days (d) 5 days
20. 20.₹533 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹205 (b) ₹328 (c) ₹369 (d) ₹41
21. 21.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 25 days (c) 9 days (d) 17 days
22. 22.3 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 4 days (d) 9 days
23. 23.9 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 8 days (d) 9 days
24. 24.₹120 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹50 (b) ₹70 (c) ₹10 (d) ₹60
25. 25.If 6 pens cost ₹96, how much do 4 pens cost? (a) ₹384 (b) ₹94 (c) ₹80 (d) ₹64
26. 26.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 26 days (d) 11 days
27. 27.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 20 days (d) 5 days
28. 28.₹84 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹84 (b) ₹42 (c) ₹72 (d) ₹12
29. 29.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 7 days (d) 10 days
30. 30.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 5 days (c) 4 days (d) 16 days
31. 31.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 15 days
32. 32.₹140 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹28 (b) ₹112 (c) ₹70 (d) ₹140
33. 33.If 2 kites cost ₹40, how much do 12 kites cost? (a) ₹50 (b) ₹260 (c) ₹480 (d) ₹240
34. 34.If 5 kites cost ₹45, how much do 2 kites cost? (a) ₹18 (b) ₹90 (c) ₹27 (d) ₹42
35. 35.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 8 days (d) 2 days
36. 36.₹116 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹116 (b) ₹87 (c) ₹58 (d) ₹29
37. 37.3 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 20 days (c) 13 days (d) 5 days
38. 38.₹111 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹111 (b) ₹37 (c) ₹74 (d) ₹75
39. 39.₹140 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹98 (b) ₹14 (c) ₹70 (d) ₹42
40. 40.₹140 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹20 (b) ₹40 (c) ₹70 (d) ₹100

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