Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 468 · 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 4 mangoes cost ₹96, how much do 10 mangoes cost? (a) ₹960 (b) ₹240 (c) ₹264 (d) ₹102
2. 2.If 2 kites cost ₹16, how much do 4 kites cost? (a) ₹40 (b) ₹32 (c) ₹64 (d) ₹18
3. 3.₹517 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹329 (b) ₹47 (c) ₹188 (d) ₹376
4. 4.If 7 kites cost ₹77, how much do 5 kites cost? (a) ₹75 (b) ₹385 (c) ₹55 (d) ₹66
5. 5.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 16 days (d) 7 days
6. 6.6 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 7 days (d) 6 days
7. 7.₹308 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹154 (b) ₹140 (c) ₹168 (d) ₹28
8. 8.If 6 pens cost ₹108, how much do 11 pens cost? (a) ₹113 (b) ₹216 (c) ₹1188 (d) ₹198
9. 9.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹198 (b) ₹165 (c) ₹231 (d) ₹33
10. 10.6 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
11. 11.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 7 days (d) 9 days
12. 12.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹65 (b) ₹117 (c) ₹104 (d) ₹13
13. 13.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 6 days (b) 3 days (c) 7 days (d) 8 days
14. 14.If 2 mangoes cost ₹16, how much do 3 mangoes cost? (a) ₹24 (b) ₹32 (c) ₹17 (d) ₹48
15. 15.If 5 mangoes cost ₹40, how much do 11 mangoes cost? (a) ₹88 (b) ₹96 (c) ₹440 (d) ₹46
16. 16.₹110 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹88 (b) ₹110 (c) ₹22 (d) ₹55
17. 17.If 9 pens cost ₹126, how much do 7 pens cost? (a) ₹124 (b) ₹112 (c) ₹882 (d) ₹98
18. 18.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 20 days (c) 21 days (d) 16 days
19. 19.₹45 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹18 (d) ₹27
20. 20.₹65 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹45 (b) ₹5 (c) ₹50 (d) ₹20
21. 21.If 2 mangoes cost ₹38, how much do 5 mangoes cost? (a) ₹190 (b) ₹114 (c) ₹95 (d) ₹41
22. 22.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 8 days (c) 10 days (d) 4 days
23. 23.₹99 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹99 (b) ₹88 (c) ₹89 (d) ₹11
24. 24.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 3 days (d) 15 days
25. 25.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 11 days (b) 6 days (c) 4 days (d) 5 days
26. 26.If 4 pens cost ₹92, how much do 5 pens cost? (a) ₹138 (b) ₹460 (c) ₹115 (d) ₹93
27. 27.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹17 (b) ₹85 (c) ₹153 (d) ₹136
28. 28.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 15 days (c) 9 days (d) 1 day
29. 29.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 6 days (d) 9 days
30. 30.9 workers can build a wall in 8 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 13 days (d) 11 days
31. 31.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 2 days (c) 15 days (d) 14 days
32. 32.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 5 days (d) 7 days
33. 33.6 workers can build a wall in 10 days. How many days will 12 workers take, working at the same speed? (a) 5 days (b) 16 days (c) 20 days (d) 4 days
34. 34.₹69 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹69 (b) ₹47 (c) ₹23 (d) ₹46
35. 35.₹156 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹156 (b) ₹39 (c) ₹78 (d) ₹117
36. 36.If 5 kites cost ₹115, how much do 2 kites cost? (a) ₹230 (b) ₹46 (c) ₹69 (d) ₹112
37. 37.If 2 pens cost ₹26, how much do 5 pens cost? (a) ₹65 (b) ₹29 (c) ₹78 (d) ₹130
38. 38.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 8 days (d) 11 days
39. 39.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 6 days (c) 4 days (d) 5 days
40. 40.₹90 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹45 (b) ₹63 (c) ₹9 (d) ₹27

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