Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 555 · 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 8 kites cost ₹104, how much do 11 kites cost? (a) ₹156 (b) ₹1144 (c) ₹143 (d) ₹107
2. 2.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 1 day (d) 9 days
3. 3.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹136 (b) ₹17 (c) ₹153 (d) ₹51
4. 4.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹115 (b) ₹23 (c) ₹161 (d) ₹138
5. 5.If 9 kites cost ₹180, how much do 7 kites cost? (a) ₹140 (b) ₹160 (c) ₹1260 (d) ₹178
6. 6.If 7 pens cost ₹126, how much do 12 pens cost? (a) ₹216 (b) ₹131 (c) ₹234 (d) ₹1512
7. 7.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 10 days (d) 3 days
8. 8.₹410 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹123 (b) ₹41 (c) ₹205 (d) ₹287
9. 9.If 8 pens cost ₹112, how much do 5 pens cost? (a) ₹70 (b) ₹560 (c) ₹109 (d) ₹84
10. 10.8 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 14 days (c) 8 days (d) 9 days
11. 11.₹273 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹156 (b) ₹195 (c) ₹39 (d) ₹117
12. 12.If 8 mangoes cost ₹32, how much do 3 mangoes cost? (a) ₹27 (b) ₹96 (c) ₹16 (d) ₹12
13. 13.₹80 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹80 (b) ₹40 (c) ₹70 (d) ₹10
14. 14.If 7 mangoes cost ₹147, how much do 3 mangoes cost? (a) ₹63 (b) ₹84 (c) ₹143 (d) ₹441
15. 15.₹376 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹141 (b) ₹235 (c) ₹47 (d) ₹188
16. 16.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹88 (b) ₹132 (c) ₹44 (d) ₹110
17. 17.₹115 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹115 (b) ₹93 (c) ₹23 (d) ₹92
18. 18.If 5 notebooks cost ₹65, how much do 8 notebooks cost? (a) ₹104 (b) ₹520 (c) ₹68 (d) ₹117
19. 19.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 7 days (c) 4 days (d) 3 days
20. 20.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 2 days (b) 8 days (c) 7 days (d) 1 day
21. 21.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 29 days (c) 28 days (d) 1 day
22. 22.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 14 days (b) 8 days (c) 12 days (d) 15 days
23. 23.If 4 mangoes cost ₹24, how much do 8 mangoes cost? (a) ₹54 (b) ₹48 (c) ₹28 (d) ₹192
24. 24.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹80 (b) ₹104 (c) ₹128 (d) ₹16
25. 25.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹80 (b) ₹16 (c) ₹96 (d) ₹112
26. 26.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 5 days (c) 14 days (d) 9 days
27. 27.₹110 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹90 (b) ₹20 (c) ₹10 (d) ₹55
28. 28.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 11 days (d) 7 days
29. 29.₹130 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹91 (b) ₹65 (c) ₹39 (d) ₹13
30. 30.If 5 notebooks cost ₹70, how much do 2 notebooks cost? (a) ₹28 (b) ₹67 (c) ₹42 (d) ₹140
31. 31.If 2 pens cost ₹30, how much do 8 pens cost? (a) ₹120 (b) ₹240 (c) ₹135 (d) ₹36
32. 32.If 6 mangoes cost ₹90, how much do 4 mangoes cost? (a) ₹88 (b) ₹75 (c) ₹60 (d) ₹360
33. 33.If 9 notebooks cost ₹171, how much do 3 notebooks cost? (a) ₹513 (b) ₹165 (c) ₹76 (d) ₹57
34. 34.If 4 kites cost ₹32, how much do 5 kites cost? (a) ₹160 (b) ₹33 (c) ₹40 (d) ₹48
35. 35.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 20 days (d) 13 days
36. 36.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 9 days (b) 3 days (c) 4 days (d) 5 days
37. 37.If 7 pens cost ₹84, how much do 4 pens cost? (a) ₹48 (b) ₹81 (c) ₹336 (d) ₹60
38. 38.If 5 kites cost ₹100, how much do 9 kites cost? (a) ₹900 (b) ₹104 (c) ₹180 (d) ₹200
39. 39.If 7 mangoes cost ₹77, how much do 4 mangoes cost? (a) ₹308 (b) ₹74 (c) ₹44 (d) ₹55
40. 40.₹160 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹80 (b) ₹40 (c) ₹160 (d) ₹120

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