Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 184 · 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 6 pens cost ₹108, how much do 3 pens cost? (a) ₹105 (b) ₹72 (c) ₹54 (d) ₹324
2. 2.₹168 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹24 (b) ₹144 (c) ₹84 (d) ₹168
3. 3.₹280 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹175 (b) ₹105 (c) ₹140 (d) ₹35
4. 4.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹430 (b) ₹86 (c) ₹387 (d) ₹43
5. 5.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 26 days (d) 15 days
6. 6.If 5 notebooks cost ₹15, how much do 7 notebooks cost? (a) ₹105 (b) ₹17 (c) ₹24 (d) ₹21
7. 7.₹40 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹8 (b) ₹20 (c) ₹40 (d) ₹32
8. 8.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 10 days (c) 7 days (d) 11 days
9. 9.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹40 (b) ₹200 (c) ₹240 (d) ₹220
10. 10.If 6 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹52 (b) ₹45 (c) ₹36 (d) ₹216
11. 11.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 4 days (d) 5 days
12. 12.If 9 mangoes cost ₹99, how much do 4 mangoes cost? (a) ₹55 (b) ₹396 (c) ₹44 (d) ₹94
13. 13.₹168 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹24 (b) ₹84 (c) ₹48 (d) ₹120
14. 14.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 2 days (c) 3 days (d) 1 day
15. 15.₹110 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹44 (b) ₹55 (c) ₹66 (d) ₹22
16. 16.If 3 kites cost ₹63, how much do 10 kites cost? (a) ₹210 (b) ₹70 (c) ₹231 (d) ₹630
17. 17.If 7 pens cost ₹133, how much do 5 pens cost? (a) ₹665 (b) ₹131 (c) ₹114 (d) ₹95
18. 18.₹154 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹77 (b) ₹88 (c) ₹22 (d) ₹66
19. 19.If 5 notebooks cost ₹95, how much do 6 notebooks cost? (a) ₹114 (b) ₹570 (c) ₹133 (d) ₹96
20. 20.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 61 days (c) 9 days (d) 60 days
21. 21.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹64 (b) ₹16 (c) ₹40 (d) ₹80
22. 22.If 2 mangoes cost ₹34, how much do 6 mangoes cost? (a) ₹119 (b) ₹204 (c) ₹102 (d) ₹38
23. 23.If 6 kites cost ₹42, how much do 12 kites cost? (a) ₹48 (b) ₹91 (c) ₹504 (d) ₹84
24. 24.If 5 notebooks cost ₹75, how much do 11 notebooks cost? (a) ₹825 (b) ₹180 (c) ₹81 (d) ₹165
25. 25.If 3 mangoes cost ₹51, how much do 5 mangoes cost? (a) ₹102 (b) ₹53 (c) ₹85 (d) ₹255
26. 26.If 3 pens cost ₹15, how much do 4 pens cost? (a) ₹25 (b) ₹16 (c) ₹60 (d) ₹20
27. 27.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 16 days (d) 4 days
28. 28.₹266 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹95 (b) ₹171 (c) ₹19 (d) ₹133
29. 29.₹275 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹150 (b) ₹25 (c) ₹175 (d) ₹125
30. 30.₹304 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹38 (b) ₹304 (c) ₹152 (d) ₹266
31. 31.4 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 16 days (b) 24 days (c) 8 days (d) 6 days
32. 32.If 2 pens cost ₹18, how much do 4 pens cost? (a) ₹20 (b) ₹36 (c) ₹72 (d) ₹45
33. 33.₹368 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹184 (b) ₹322 (c) ₹368 (d) ₹46
34. 34.If 4 notebooks cost ₹56, how much do 10 notebooks cost? (a) ₹140 (b) ₹560 (c) ₹62 (d) ₹154
35. 35.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 5 days (c) 3 days (d) 4 days
36. 36.If 4 pens cost ₹84, how much do 8 pens cost? (a) ₹672 (b) ₹189 (c) ₹168 (d) ₹88
37. 37.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹26 (b) ₹39 (c) ₹52 (d) ₹78
38. 38.If 8 mangoes cost ₹136, how much do 9 mangoes cost? (a) ₹170 (b) ₹153 (c) ₹137 (d) ₹1224
39. 39.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 1 day (d) 10 days
40. 40.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 11 days (d) 17 days

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