Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 342 · 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 ₹189, how much do 12 kites cost? (a) ₹2268 (b) ₹252 (c) ₹192 (d) ₹273
2. 2.₹380 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹380 (b) ₹342 (c) ₹190 (d) ₹38
3. 3.If 9 kites cost ₹144, how much do 5 kites cost? (a) ₹96 (b) ₹140 (c) ₹80 (d) ₹720
4. 4.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 21 days (d) 9 days
5. 5.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 6 days (d) 4 days
6. 6.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 3 days (d) 8 days
7. 7.If 5 mangoes cost ₹55, how much do 6 mangoes cost? (a) ₹66 (b) ₹77 (c) ₹330 (d) ₹56
8. 8.If 2 mangoes cost ₹38, how much do 6 mangoes cost? (a) ₹42 (b) ₹114 (c) ₹228 (d) ₹133
9. 9.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 17 days (d) 13 days
10. 10.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹96 (d) ₹78
11. 11.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 13 days (d) 16 days
12. 12.If 2 mangoes cost ₹16, how much do 3 mangoes cost? (a) ₹17 (b) ₹48 (c) ₹32 (d) ₹24
13. 13.₹20 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹15 (b) ₹10 (c) ₹5 (d) ₹20
14. 14.If 9 kites cost ₹117, how much do 11 kites cost? (a) ₹143 (b) ₹1287 (c) ₹156 (d) ₹119
15. 15.₹270 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹30 (b) ₹240 (c) ₹135 (d) ₹270
16. 16.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 10 days (d) 6 days
17. 17.If 4 mangoes cost ₹100, how much do 7 mangoes cost? (a) ₹175 (b) ₹103 (c) ₹200 (d) ₹700
18. 18.₹195 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹39 (b) ₹195 (c) ₹156 (d) ₹157
19. 19.If 5 notebooks cost ₹120, how much do 6 notebooks cost? (a) ₹121 (b) ₹720 (c) ₹168 (d) ₹144
20. 20.₹98 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹49 (b) ₹98 (c) ₹14 (d) ₹84
21. 21.7 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) 14 days (d) 15 days
22. 22.₹168 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹168 (b) ₹84 (c) ₹147 (d) ₹21
23. 23.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 13 days (c) 15 days (d) 12 days
24. 24.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 9 days
25. 25.If 6 pens cost ₹42, how much do 12 pens cost? (a) ₹504 (b) ₹48 (c) ₹84 (d) ₹91
26. 26.₹245 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹175 (b) ₹210 (c) ₹35 (d) ₹70
27. 27.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 10 days (d) 18 days
28. 28.If 7 pens cost ₹21, how much do 10 pens cost? (a) ₹24 (b) ₹33 (c) ₹30 (d) ₹210
29. 29.₹216 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹90 (b) ₹108 (c) ₹18 (d) ₹126
30. 30.If 2 kites cost ₹36, how much do 3 kites cost? (a) ₹37 (b) ₹108 (c) ₹72 (d) ₹54
31. 31.If 7 notebooks cost ₹63, how much do 4 notebooks cost? (a) ₹252 (b) ₹45 (c) ₹36 (d) ₹60
32. 32.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 11 days (c) 5 days (d) 16 days
33. 33.If 2 pens cost ₹44, how much do 12 pens cost? (a) ₹54 (b) ₹528 (c) ₹264 (d) ₹286
34. 34.If 7 kites cost ₹35, how much do 4 kites cost? (a) ₹25 (b) ₹32 (c) ₹140 (d) ₹20
35. 35.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹80 (b) ₹20 (c) ₹60 (d) ₹100
36. 36.If 3 mangoes cost ₹72, how much do 10 mangoes cost? (a) ₹79 (b) ₹720 (c) ₹240 (d) ₹264
37. 37.If 9 pens cost ₹108, how much do 11 pens cost? (a) ₹110 (b) ₹144 (c) ₹132 (d) ₹1188
38. 38.₹57 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹57 (b) ₹19 (c) ₹39 (d) ₹38
39. 39.₹132 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹66 (b) ₹12 (c) ₹36 (d) ₹96
40. 40.₹48 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹12 (c) ₹36 (d) ₹24

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