Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 768 · 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.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹252 (b) ₹140 (c) ₹28 (d) ₹196
2. 2.₹112 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹98 (b) ₹112 (c) ₹14 (d) ₹56
3. 3.If 6 notebooks cost ₹18, how much do 10 notebooks cost? (a) ₹33 (b) ₹22 (c) ₹180 (d) ₹30
4. 4.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 3 days (d) 10 days
5. 5.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 11 days (b) 28 days (c) 19 days (d) 27 days
6. 6.If 6 notebooks cost ₹114, how much do 7 notebooks cost? (a) ₹798 (b) ₹115 (c) ₹133 (d) ₹152
7. 7.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 13 days (d) 15 days
8. 8.If 2 mangoes cost ₹20, how much do 11 mangoes cost? (a) ₹120 (b) ₹220 (c) ₹29 (d) ₹110
9. 9.₹121 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹11 (b) ₹110 (c) ₹99 (d) ₹22
10. 10.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 18 days (c) 10 days (d) 42 days
11. 11.If 3 notebooks cost ₹9, how much do 10 notebooks cost? (a) ₹33 (b) ₹16 (c) ₹90 (d) ₹30
12. 12.₹243 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹217 (b) ₹27 (c) ₹243 (d) ₹216
13. 13.If 8 kites cost ₹80, how much do 2 kites cost? (a) ₹74 (b) ₹30 (c) ₹160 (d) ₹20
14. 14.₹550 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹275 (b) ₹150 (c) ₹50 (d) ₹400
15. 15.If 8 pens cost ₹128, how much do 7 pens cost? (a) ₹127 (b) ₹896 (c) ₹128 (d) ₹112
16. 16.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 9 days (d) 4 days
17. 17.If 2 pens cost ₹6, how much do 3 pens cost? (a) ₹18 (b) ₹9 (c) ₹12 (d) ₹7
18. 18.If 5 notebooks cost ₹55, how much do 10 notebooks cost? (a) ₹550 (b) ₹60 (c) ₹121 (d) ₹110
19. 19.If 4 notebooks cost ₹16, how much do 12 notebooks cost? (a) ₹52 (b) ₹24 (c) ₹192 (d) ₹48
20. 20.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 8 days (d) 15 days
21. 21.If 4 pens cost ₹88, how much do 6 pens cost? (a) ₹528 (b) ₹154 (c) ₹90 (d) ₹132
22. 22.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 10 days (c) 16 days (d) 1 day
23. 23.₹30 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹12 (b) ₹15 (c) ₹6 (d) ₹18
24. 24.If 6 notebooks cost ₹90, how much do 5 notebooks cost? (a) ₹450 (b) ₹90 (c) ₹75 (d) ₹89
25. 25.₹120 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹84 (d) ₹36
26. 26.If 6 pens cost ₹138, how much do 7 pens cost? (a) ₹139 (b) ₹966 (c) ₹184 (d) ₹161
27. 27.If 5 mangoes cost ₹95, how much do 6 mangoes cost? (a) ₹114 (b) ₹96 (c) ₹570 (d) ₹133
28. 28.If 4 pens cost ₹40, how much do 2 pens cost? (a) ₹80 (b) ₹38 (c) ₹30 (d) ₹20
29. 29.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 12 days (c) 2 days (d) 10 days
30. 30.If 6 notebooks cost ₹84, how much do 3 notebooks cost? (a) ₹252 (b) ₹81 (c) ₹42 (d) ₹56
31. 31.If 7 mangoes cost ₹42, how much do 12 mangoes cost? (a) ₹47 (b) ₹78 (c) ₹72 (d) ₹504
32. 32.If 4 kites cost ₹48, how much do 5 kites cost? (a) ₹240 (b) ₹72 (c) ₹49 (d) ₹60
33. 33.5 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) 6 days (d) 5 days
34. 34.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹258 (b) ₹43 (c) ₹215 (d) ₹301
35. 35.If 6 notebooks cost ₹102, how much do 11 notebooks cost? (a) ₹187 (b) ₹204 (c) ₹1122 (d) ₹107
36. 36.8 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 60 days (b) 9 days (c) 61 days (d) 21 days
37. 37.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 7 days (c) 39 days (d) 40 days
38. 38.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 22 days (c) 15 days (d) 21 days
39. 39.₹208 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹128 (b) ₹16 (c) ₹104 (d) ₹80
40. 40.6 workers can build a wall in 12 days. How many days will 8 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 9 days (d) 16 days

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