Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 436 · 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.₹160 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹160 (b) ₹80 (c) ₹32 (d) ₹128
2. 2.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 9 days (d) 8 days
3. 3.₹24 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹12 (b) ₹24 (c) ₹8 (d) ₹16
4. 4.₹416 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹32 (b) ₹208 (c) ₹256 (d) ₹160
5. 5.₹462 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹294 (b) ₹231 (c) ₹168 (d) ₹42
6. 6.₹126 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹126 (b) ₹63 (c) ₹112 (d) ₹14
7. 7.8 workers can build a wall in 11 days. How many days will 4 workers take, working at the same speed? (a) 22 days (b) 15 days (c) 23 days (d) 7 days
8. 8.If 2 notebooks cost ₹30, how much do 3 notebooks cost? (a) ₹60 (b) ₹31 (c) ₹45 (d) ₹90
9. 9.If 6 notebooks cost ₹150, how much do 9 notebooks cost? (a) ₹1350 (b) ₹225 (c) ₹153 (d) ₹250
10. 10.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹11 (b) ₹55 (c) ₹66 (d) ₹44
11. 11.If 2 pens cost ₹22, how much do 4 pens cost? (a) ₹44 (b) ₹88 (c) ₹24 (d) ₹55
12. 12.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 14 days (d) 8 days
13. 13.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹52 (b) ₹13 (c) ₹65 (d) ₹78
14. 14.6 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 36 days (c) 8 days (d) 16 days
15. 15.If 7 pens cost ₹56, how much do 12 pens cost? (a) ₹672 (b) ₹96 (c) ₹104 (d) ₹61
16. 16.₹280 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹28 (b) ₹252 (c) ₹280 (d) ₹140
17. 17.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 8 days (d) 7 days
18. 18.If 6 notebooks cost ₹48, how much do 3 notebooks cost? (a) ₹144 (b) ₹24 (c) ₹45 (d) ₹32
19. 19.If 2 kites cost ₹14, how much do 6 kites cost? (a) ₹18 (b) ₹49 (c) ₹42 (d) ₹84
20. 20.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 17 days (b) 8 days (c) 11 days (d) 9 days
21. 21.If 4 notebooks cost ₹12, how much do 8 notebooks cost? (a) ₹27 (b) ₹24 (c) ₹16 (d) ₹96
22. 22.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 40 days (b) 19 days (c) 7 days (d) 39 days
23. 23.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 1 day (c) 29 days (d) 28 days
24. 24.If 7 mangoes cost ₹161, how much do 10 mangoes cost? (a) ₹1610 (b) ₹253 (c) ₹164 (d) ₹230
25. 25.₹494 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹304 (b) ₹247 (c) ₹38 (d) ₹190
26. 26.If 4 pens cost ₹36, how much do 8 pens cost? (a) ₹40 (b) ₹72 (c) ₹288 (d) ₹81
27. 27.If 9 mangoes cost ₹108, how much do 7 mangoes cost? (a) ₹84 (b) ₹96 (c) ₹106 (d) ₹756
28. 28.3 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
29. 29.If 3 kites cost ₹57, how much do 11 kites cost? (a) ₹209 (b) ₹627 (c) ₹65 (d) ₹228
30. 30.If 2 kites cost ₹20, how much do 6 kites cost? (a) ₹60 (b) ₹24 (c) ₹70 (d) ₹120
31. 31.₹363 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹198 (b) ₹33 (c) ₹231 (d) ₹165
32. 32.If 2 kites cost ₹18, how much do 8 kites cost? (a) ₹72 (b) ₹81 (c) ₹144 (d) ₹24
33. 33.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 21 days (c) 11 days (d) 20 days
34. 34.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 9 days (d) 8 days
35. 35.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹28 (b) ₹7 (c) ₹49 (d) ₹56
36. 36.If 4 mangoes cost ₹12, how much do 5 mangoes cost? (a) ₹13 (b) ₹18 (c) ₹60 (d) ₹15
37. 37.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 16 days (d) 17 days
38. 38.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 1 day (b) 6 days (c) 7 days (d) 5 days
39. 39.If 3 mangoes cost ₹27, how much do 9 mangoes cost? (a) ₹33 (b) ₹243 (c) ₹90 (d) ₹81
40. 40.5 workers can build a wall in 12 days. How many days will 10 workers take, working at the same speed? (a) 24 days (b) 6 days (c) 17 days (d) 7 days

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