Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 22 · 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 9 kites cost ₹216, how much do 11 kites cost? (a) ₹2376 (b) ₹288 (c) ₹218 (d) ₹264
2. 2.If 6 kites cost ₹144, how much do 9 kites cost? (a) ₹147 (b) ₹1296 (c) ₹216 (d) ₹240
3. 3.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 13 days (c) 27 days (d) 5 days
4. 4.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹299 (b) ₹46 (c) ₹414 (d) ₹184
5. 5.If 3 mangoes cost ₹45, how much do 4 mangoes cost? (a) ₹46 (b) ₹75 (c) ₹60 (d) ₹180
6. 6.₹240 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹24 (b) ₹216 (c) ₹240 (d) ₹120
7. 7.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 10 days (c) 8 days (d) 9 days
8. 8.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 26 days (d) 27 days
9. 9.₹168 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹84 (b) ₹12 (c) ₹108 (d) ₹60
10. 10.If 5 kites cost ₹20, how much do 9 kites cost? (a) ₹36 (b) ₹24 (c) ₹40 (d) ₹180
11. 11.If 3 kites cost ₹48, how much do 4 kites cost? (a) ₹49 (b) ₹80 (c) ₹64 (d) ₹192
12. 12.3 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 6 days (d) 7 days
13. 13.If 2 notebooks cost ₹46, how much do 5 notebooks cost? (a) ₹115 (b) ₹230 (c) ₹49 (d) ₹138
14. 14.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 5 days (d) 16 days
15. 15.If 3 notebooks cost ₹66, how much do 6 notebooks cost? (a) ₹132 (b) ₹154 (c) ₹396 (d) ₹69
16. 16.₹36 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹27 (b) ₹36 (c) ₹18 (d) ₹9
17. 17.₹176 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹48 (b) ₹88 (c) ₹128 (d) ₹16
18. 18.If 4 kites cost ₹84, how much do 10 kites cost? (a) ₹210 (b) ₹90 (c) ₹231 (d) ₹840
19. 19.₹108 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹81 (b) ₹54 (c) ₹108 (d) ₹27
20. 20.₹225 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹90 (b) ₹180 (c) ₹45 (d) ₹135
21. 21.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 9 days (c) 16 days (d) 15 days
22. 22.₹140 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹80 (b) ₹20 (c) ₹60 (d) ₹70
23. 23.If 9 notebooks cost ₹36, how much do 7 notebooks cost? (a) ₹32 (b) ₹252 (c) ₹28 (d) ₹34
24. 24.₹400 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹50 (b) ₹350 (c) ₹200 (d) ₹400
25. 25.₹363 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹33 (b) ₹264 (c) ₹231 (d) ₹132
26. 26.₹115 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹92 (b) ₹23 (c) ₹46 (d) ₹69
27. 27.₹65 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹50 (b) ₹20 (c) ₹45 (d) ₹5
28. 28.If 8 kites cost ₹80, how much do 11 kites cost? (a) ₹880 (b) ₹120 (c) ₹83 (d) ₹110
29. 29.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 9 days
30. 30.₹216 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹81 (b) ₹135 (c) ₹27 (d) ₹108
31. 31.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 5 days (c) 3 days (d) 4 days
32. 32.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 3 days (d) 5 days
33. 33.If 7 kites cost ₹105, how much do 6 kites cost? (a) ₹90 (b) ₹105 (c) ₹630 (d) ₹104
34. 34.If 9 notebooks cost ₹27, how much do 5 notebooks cost? (a) ₹135 (b) ₹18 (c) ₹23 (d) ₹15
35. 35.If 9 notebooks cost ₹99, how much do 10 notebooks cost? (a) ₹121 (b) ₹990 (c) ₹100 (d) ₹110
36. 36.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 13 days (d) 26 days
37. 37.₹261 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹29 (b) ₹58 (c) ₹203 (d) ₹232
38. 38.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹301 (b) ₹258 (c) ₹43 (d) ₹215
39. 39.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 39 days (c) 19 days (d) 7 days
40. 40.If 3 notebooks cost ₹18, how much do 2 notebooks cost? (a) ₹12 (b) ₹36 (c) ₹18 (d) ₹17

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