Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 759 · 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 6 pens cost ₹24, how much do 9 pens cost? (a) ₹40 (b) ₹36 (c) ₹27 (d) ₹216
2. 2.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 36 days (b) 4 days (c) 18 days (d) 6 days
3. 3.₹81 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹72 (b) ₹18 (c) ₹9 (d) ₹63
4. 4.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 2 days (c) 24 days (d) 25 days
5. 5.If 2 notebooks cost ₹22, how much do 6 notebooks cost? (a) ₹132 (b) ₹26 (c) ₹66 (d) ₹77
6. 6.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹182 (b) ₹156 (c) ₹130 (d) ₹26
7. 7.₹50 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹5 (b) ₹35 (c) ₹15 (d) ₹25
8. 8.If 7 mangoes cost ₹133, how much do 5 mangoes cost? (a) ₹95 (b) ₹665 (c) ₹114 (d) ₹131
9. 9.If 5 pens cost ₹30, how much do 6 pens cost? (a) ₹31 (b) ₹180 (c) ₹42 (d) ₹36
10. 10.If 8 notebooks cost ₹120, how much do 12 notebooks cost? (a) ₹195 (b) ₹124 (c) ₹180 (d) ₹1440
11. 11.If 8 pens cost ₹160, how much do 2 pens cost? (a) ₹320 (b) ₹60 (c) ₹40 (d) ₹154
12. 12.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 13 days (d) 12 days
13. 13.If 8 mangoes cost ₹56, how much do 7 mangoes cost? (a) ₹392 (b) ₹49 (c) ₹56 (d) ₹55
14. 14.If 3 pens cost ₹57, how much do 6 pens cost? (a) ₹133 (b) ₹342 (c) ₹60 (d) ₹114
15. 15.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹47 (b) ₹329 (c) ₹283 (d) ₹282
16. 16.8 workers can build a wall in 6 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 12 days (d) 3 days
17. 17.If 9 mangoes cost ₹171, how much do 3 mangoes cost? (a) ₹165 (b) ₹513 (c) ₹76 (d) ₹57
18. 18.If 2 pens cost ₹24, how much do 4 pens cost? (a) ₹48 (b) ₹96 (c) ₹26 (d) ₹60
19. 19.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 9 days (c) 12 days (d) 7 days
20. 20.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 6 days (d) 5 days
21. 21.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 7 days (d) 6 days
22. 22.₹333 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹333 (b) ₹37 (c) ₹296 (d) ₹297
23. 23.If 4 kites cost ₹56, how much do 8 kites cost? (a) ₹126 (b) ₹60 (c) ₹448 (d) ₹112
24. 24.5 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
25. 25.9 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 36 days (b) 15 days (c) 37 days (d) 1 day
26. 26.If 9 notebooks cost ₹63, how much do 2 notebooks cost? (a) ₹14 (b) ₹21 (c) ₹56 (d) ₹126
27. 27.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 19 days (d) 11 days
28. 28.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹80 (b) ₹128 (c) ₹16 (d) ₹104
29. 29.6 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 8 days (d) 10 days
30. 30.If 9 pens cost ₹126, how much do 2 pens cost? (a) ₹42 (b) ₹252 (c) ₹119 (d) ₹28
31. 31.If 5 kites cost ₹60, how much do 7 kites cost? (a) ₹62 (b) ₹96 (c) ₹84 (d) ₹420
32. 32.₹224 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹32 (b) ₹128 (c) ₹96 (d) ₹112
33. 33.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 7 days (d) 3 days
34. 34.₹168 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹24 (b) ₹72 (c) ₹84 (d) ₹96
35. 35.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 10 days (c) 14 days (d) 15 days
36. 36.If 2 notebooks cost ₹30, how much do 4 notebooks cost? (a) ₹75 (b) ₹120 (c) ₹32 (d) ₹60
37. 37.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 15 days (d) 26 days
38. 38.₹234 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹39 (b) ₹195 (c) ₹234 (d) ₹117
39. 39.₹96 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹16 (d) ₹80
40. 40.₹96 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹96 (b) ₹84 (c) ₹48 (d) ₹12

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