Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 395 · 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. 1.9 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 18 days (c) 16 days (d) 19 days
2. 2.₹49 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹7 (b) ₹43 (c) ₹49 (d) ₹42
3. 3.If 7 mangoes cost ₹70, how much do 11 mangoes cost? (a) ₹74 (b) ₹770 (c) ₹120 (d) ₹110
4. 4.4 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 18 days (d) 19 days
5. 5.If 2 pens cost ₹16, how much do 5 pens cost? (a) ₹19 (b) ₹48 (c) ₹40 (d) ₹80
6. 6.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 4 days (c) 5 days (d) 36 days
7. 7.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 49 days (d) 19 days
8. 8.If 7 notebooks cost ₹119, how much do 9 notebooks cost? (a) ₹153 (b) ₹121 (c) ₹170 (d) ₹1071
9. 9.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 23 days (c) 25 days (d) 12 days
10. 10.₹272 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹272 (b) ₹136 (c) ₹34 (d) ₹238
11. 11.If 2 mangoes cost ₹14, how much do 8 mangoes cost? (a) ₹63 (b) ₹20 (c) ₹112 (d) ₹56
12. 12.₹299 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹207 (b) ₹230 (c) ₹92 (d) ₹23
13. 13.If 9 mangoes cost ₹108, how much do 4 mangoes cost? (a) ₹432 (b) ₹48 (c) ₹103 (d) ₹60
14. 14.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 13 days (c) 28 days (d) 29 days
15. 15.If 4 pens cost ₹52, how much do 5 pens cost? (a) ₹53 (b) ₹65 (c) ₹78 (d) ₹260
16. 16.If 7 mangoes cost ₹42, how much do 5 mangoes cost? (a) ₹210 (b) ₹40 (c) ₹30 (d) ₹36
17. 17.If 5 mangoes cost ₹115, how much do 4 mangoes cost? (a) ₹92 (b) ₹460 (c) ₹115 (d) ₹114
18. 18.If 8 pens cost ₹136, how much do 6 pens cost? (a) ₹816 (b) ₹119 (c) ₹134 (d) ₹102
19. 19.5 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 4 days (c) 7 days (d) 25 days
20. 20.₹87 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹29 (b) ₹87 (c) ₹58 (d) ₹59
21. 21.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 36 days (b) 6 days (c) 18 days (d) 4 days
22. 22.₹624 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹192 (b) ₹432 (c) ₹312 (d) ₹48
23. 23.₹85 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹34 (b) ₹17 (c) ₹68 (d) ₹51
24. 24.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 11 days (c) 13 days (d) 12 days
25. 25.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 5 days (d) 20 days
26. 26.5 workers can build a wall in 4 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 9 days (d) 2 days
27. 27.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 40 days (c) 9 days (d) 39 days
28. 28.If 4 notebooks cost ₹12, how much do 3 notebooks cost? (a) ₹12 (b) ₹11 (c) ₹36 (d) ₹9
29. 29.If 5 pens cost ₹125, how much do 10 pens cost? (a) ₹130 (b) ₹275 (c) ₹250 (d) ₹1250
30. 30.If 7 mangoes cost ₹84, how much do 6 mangoes cost? (a) ₹83 (b) ₹504 (c) ₹84 (d) ₹72
31. 31.If 5 notebooks cost ₹55, how much do 4 notebooks cost? (a) ₹44 (b) ₹220 (c) ₹55 (d) ₹54
32. 32.If 3 mangoes cost ₹57, how much do 7 mangoes cost? (a) ₹152 (b) ₹133 (c) ₹399 (d) ₹61
33. 33.If 2 notebooks cost ₹36, how much do 9 notebooks cost? (a) ₹324 (b) ₹162 (c) ₹43 (d) ₹180
34. 34.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 12 days (d) 20 days
35. 35.If 9 mangoes cost ₹36, how much do 7 mangoes cost? (a) ₹34 (b) ₹32 (c) ₹252 (d) ₹28
36. 36.If 5 mangoes cost ₹50, how much do 6 mangoes cost? (a) ₹51 (b) ₹60 (c) ₹300 (d) ₹70
37. 37.₹256 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹128 (b) ₹160 (c) ₹32 (d) ₹96
38. 38.If 7 kites cost ₹126, how much do 8 kites cost? (a) ₹127 (b) ₹1008 (c) ₹162 (d) ₹144
39. 39.If 3 notebooks cost ₹12, how much do 5 notebooks cost? (a) ₹14 (b) ₹20 (c) ₹60 (d) ₹24
40. 40.If 5 kites cost ₹60, how much do 7 kites cost? (a) ₹420 (b) ₹96 (c) ₹84 (d) ₹62

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