Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 907 · 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.₹75 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹75 (b) ₹61 (c) ₹15 (d) ₹60
2. 2.If 4 kites cost ₹28, how much do 9 kites cost? (a) ₹33 (b) ₹252 (c) ₹63 (d) ₹70
3. 3.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 40 days (c) 17 days (d) 39 days
4. 4.₹123 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹123 (b) ₹41 (c) ₹82 (d) ₹83
5. 5.If 3 mangoes cost ₹54, how much do 4 mangoes cost? (a) ₹72 (b) ₹55 (c) ₹216 (d) ₹90
6. 6.If 3 pens cost ₹36, how much do 4 pens cost? (a) ₹48 (b) ₹37 (c) ₹144 (d) ₹60
7. 7.₹143 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹104 (b) ₹91 (c) ₹52 (d) ₹13
8. 8.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹252 (b) ₹28 (c) ₹140 (d) ₹196
9. 9.₹169 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹65 (b) ₹117 (c) ₹104 (d) ₹13
10. 10.If 5 pens cost ₹15, how much do 2 pens cost? (a) ₹9 (b) ₹12 (c) ₹30 (d) ₹6
11. 11.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹44 (b) ₹8 (c) ₹48 (d) ₹40
12. 12.₹624 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹240 (b) ₹312 (c) ₹48 (d) ₹384
13. 13.If 3 kites cost ₹60, how much do 7 kites cost? (a) ₹140 (b) ₹420 (c) ₹160 (d) ₹64
14. 14.4 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
15. 15.If 2 notebooks cost ₹16, how much do 8 notebooks cost? (a) ₹64 (b) ₹72 (c) ₹128 (d) ₹22
16. 16.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹150 (c) ₹120 (d) ₹135
17. 17.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 13 days (c) 8 days (d) 11 days
18. 18.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 21 days (d) 1 day
19. 19.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 24 days (c) 10 days (d) 6 days
20. 20.If 3 pens cost ₹9, how much do 4 pens cost? (a) ₹10 (b) ₹36 (c) ₹12 (d) ₹15
21. 21.₹80 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹32 (b) ₹40 (c) ₹16 (d) ₹48
22. 22.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 7 days (d) 6 days
23. 23.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 15 days (c) 16 days (d) 1 day
24. 24.If 8 mangoes cost ₹64, how much do 2 mangoes cost? (a) ₹24 (b) ₹128 (c) ₹16 (d) ₹58
25. 25.If 8 pens cost ₹128, how much do 3 pens cost? (a) ₹123 (b) ₹64 (c) ₹48 (d) ₹384
26. 26.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹187 (b) ₹170 (c) ₹34 (d) ₹204
27. 27.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 5 days (c) 20 days (d) 21 days
28. 28.₹99 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹18 (b) ₹90 (c) ₹81 (d) ₹9
29. 29.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 6 days (d) 7 days
30. 30.₹143 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹99 (b) ₹110 (c) ₹11 (d) ₹44
31. 31.₹336 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹168 (b) ₹24 (c) ₹216 (d) ₹120
32. 32.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 7 days (b) 28 days (c) 10 days (d) 18 days
33. 33.₹81 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹55 (b) ₹54 (c) ₹81 (d) ₹27
34. 34.9 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 34 days (c) 33 days (d) 5 days
35. 35.If 7 notebooks cost ₹133, how much do 11 notebooks cost? (a) ₹137 (b) ₹1463 (c) ₹228 (d) ₹209
36. 36.6 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 27 days (c) 13 days (d) 3 days
37. 37.₹308 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹264 (b) ₹308 (c) ₹154 (d) ₹44
38. 38.₹88 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹8 (b) ₹64 (c) ₹24 (d) ₹44
39. 39.If 2 mangoes cost ₹36, how much do 10 mangoes cost? (a) ₹198 (b) ₹360 (c) ₹44 (d) ₹180
40. 40.If 8 pens cost ₹120, how much do 9 pens cost? (a) ₹150 (b) ₹1080 (c) ₹121 (d) ₹135

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