Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 304 · 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.₹64 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹32 (b) ₹64 (c) ₹48 (d) ₹16
2. 2.If 7 pens cost ₹98, how much do 8 pens cost? (a) ₹126 (b) ₹99 (c) ₹112 (d) ₹784
3. 3.If 9 pens cost ₹72, how much do 6 pens cost? (a) ₹69 (b) ₹432 (c) ₹56 (d) ₹48
4. 4.₹440 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹40 (b) ₹320 (c) ₹220 (d) ₹120
5. 5.If 8 kites cost ₹184, how much do 9 kites cost? (a) ₹230 (b) ₹185 (c) ₹1656 (d) ₹207
6. 6.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹56 (b) ₹42 (c) ₹14 (d) ₹28
7. 7.If 4 pens cost ₹64, how much do 9 pens cost? (a) ₹69 (b) ₹576 (c) ₹144 (d) ₹160
8. 8.₹473 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹43 (b) ₹172 (c) ₹301 (d) ₹344
9. 9.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹192 (b) ₹48 (c) ₹240 (d) ₹216
10. 10.₹50 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹5 (b) ₹35 (c) ₹25 (d) ₹15
11. 11.₹234 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹18 (b) ₹117 (c) ₹162 (d) ₹72
12. 12.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 10 days (d) 11 days
13. 13.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 12 days (c) 9 days (d) 7 days
14. 14.If 4 mangoes cost ₹96, how much do 7 mangoes cost? (a) ₹168 (b) ₹672 (c) ₹99 (d) ₹192
15. 15.₹80 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹80 (b) ₹64 (c) ₹40 (d) ₹16
16. 16.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 3 days (d) 2 days
17. 17.If 5 mangoes cost ₹90, how much do 4 mangoes cost? (a) ₹89 (b) ₹72 (c) ₹360 (d) ₹90
18. 18.₹550 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹350 (b) ₹50 (c) ₹200 (d) ₹275
19. 19.₹188 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹188 (b) ₹141 (c) ₹47 (d) ₹94
20. 20.If 5 pens cost ₹75, how much do 10 pens cost? (a) ₹750 (b) ₹165 (c) ₹150 (d) ₹80
21. 21.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 11 days (d) 3 days
22. 22.If 4 kites cost ₹56, how much do 5 kites cost? (a) ₹70 (b) ₹57 (c) ₹280 (d) ₹84
23. 23.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 6 days (b) 19 days (c) 18 days (d) 12 days
24. 24.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹296 (b) ₹148 (c) ₹259 (d) ₹37
25. 25.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 15 days (c) 16 days (d) 14 days
26. 26.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 2 days (d) 19 days
27. 27.If 8 notebooks cost ₹96, how much do 3 notebooks cost? (a) ₹91 (b) ₹288 (c) ₹48 (d) ₹36
28. 28.If 5 kites cost ₹45, how much do 6 kites cost? (a) ₹63 (b) ₹54 (c) ₹46 (d) ₹270
29. 29.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 4 days (d) 6 days
30. 30.₹165 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹150 (b) ₹30 (c) ₹15 (d) ₹135
31. 31.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹14 (c) ₹21 (d) ₹7
32. 32.If 5 notebooks cost ₹100, how much do 4 notebooks cost? (a) ₹100 (b) ₹400 (c) ₹99 (d) ₹80
33. 33.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 28 days (c) 27 days (d) 11 days
34. 34.If 7 pens cost ₹84, how much do 9 pens cost? (a) ₹120 (b) ₹108 (c) ₹86 (d) ₹756
35. 35.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 45 days (b) 21 days (c) 5 days (d) 9 days
36. 36.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 25 days (d) 4 days
37. 37.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹147 (b) ₹42 (c) ₹21 (d) ₹168
38. 38.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 17 days (d) 6 days
39. 39.₹448 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹32 (b) ₹160 (c) ₹224 (d) ₹288
40. 40.₹250 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹50 (b) ₹125 (c) ₹100 (d) ₹150

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