Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 51 · 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 ₹153, how much do 3 kites cost? (a) ₹51 (b) ₹147 (c) ₹68 (d) ₹459
2. 2.If 3 pens cost ₹63, how much do 11 pens cost? (a) ₹71 (b) ₹252 (c) ₹693 (d) ₹231
3. 3.If 2 mangoes cost ₹32, how much do 3 mangoes cost? (a) ₹64 (b) ₹33 (c) ₹96 (d) ₹48
4. 4.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 14 days (d) 9 days
5. 5.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 12 days (c) 24 days (d) 25 days
6. 6.If 5 mangoes cost ₹70, how much do 6 mangoes cost? (a) ₹98 (b) ₹71 (c) ₹420 (d) ₹84
7. 7.₹108 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹48 (b) ₹54 (c) ₹60 (d) ₹12
8. 8.₹700 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹350 (b) ₹450 (c) ₹250 (d) ₹50
9. 9.₹99 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹72 (b) ₹81 (c) ₹9 (d) ₹27
10. 10.If 4 mangoes cost ₹84, how much do 10 mangoes cost? (a) ₹231 (b) ₹90 (c) ₹840 (d) ₹210
11. 11.If 5 kites cost ₹60, how much do 10 kites cost? (a) ₹600 (b) ₹132 (c) ₹120 (d) ₹65
12. 12.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 4 days (d) 25 days
13. 13.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 9 days (d) 25 days
14. 14.₹550 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹50 (b) ₹250 (c) ₹275 (d) ₹300
15. 15.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 19 days (d) 2 days
16. 16.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹115 (b) ₹161 (c) ₹23 (d) ₹138
17. 17.If 7 pens cost ₹126, how much do 10 pens cost? (a) ₹180 (b) ₹198 (c) ₹129 (d) ₹1260
18. 18.₹174 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹145 (b) ₹29 (c) ₹87 (d) ₹174
19. 19.₹306 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹136 (b) ₹34 (c) ₹153 (d) ₹170
20. 20.If 4 mangoes cost ₹76, how much do 6 mangoes cost? (a) ₹78 (b) ₹133 (c) ₹456 (d) ₹114
21. 21.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 17 days (c) 5 days (d) 6 days
22. 22.₹153 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹119 (b) ₹17 (c) ₹34 (d) ₹136
23. 23.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 17 days (b) 22 days (c) 13 days (d) 21 days
24. 24.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹203 (b) ₹29 (c) ₹174 (d) ₹145
25. 25.If 9 mangoes cost ₹216, how much do 3 mangoes cost? (a) ₹648 (b) ₹72 (c) ₹96 (d) ₹210
26. 26.6 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 15 days (d) 9 days
27. 27.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 8 days (c) 7 days (d) 9 days
28. 28.₹110 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹80 (b) ₹55 (c) ₹30 (d) ₹10
29. 29.₹21 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹15 (b) ₹21 (c) ₹7 (d) ₹14
30. 30.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 4 days (d) 3 days
31. 31.₹380 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹380 (b) ₹342 (c) ₹38 (d) ₹190
32. 32.If 4 notebooks cost ₹12, how much do 8 notebooks cost? (a) ₹24 (b) ₹27 (c) ₹16 (d) ₹96
33. 33.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 28 days (b) 8 days (c) 20 days (d) 7 days
34. 34.If 2 kites cost ₹44, how much do 12 kites cost? (a) ₹54 (b) ₹286 (c) ₹264 (d) ₹528
35. 35.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 22 days (c) 23 days (d) 13 days
36. 36.If 4 pens cost ₹12, how much do 8 pens cost? (a) ₹16 (b) ₹96 (c) ₹24 (d) ₹27
37. 37.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 4 days (d) 10 days
38. 38.If 8 mangoes cost ₹64, how much do 3 mangoes cost? (a) ₹192 (b) ₹59 (c) ₹32 (d) ₹24
39. 39.₹144 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹24 (b) ₹144 (c) ₹120 (d) ₹72
40. 40.If 3 mangoes cost ₹33, how much do 8 mangoes cost? (a) ₹38 (b) ₹88 (c) ₹264 (d) ₹99

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