Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 860 · 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 7 notebooks cost ₹98, how much do 11 notebooks cost? (a) ₹154 (b) ₹102 (c) ₹1078 (d) ₹168
2. 2.If 9 mangoes cost ₹117, how much do 5 mangoes cost? (a) ₹113 (b) ₹65 (c) ₹585 (d) ₹78
3. 3.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 3 days (d) 5 days
4. 4.3 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 21 days (d) 22 days
5. 5.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 5 days (d) 6 days
6. 6.If 4 notebooks cost ₹48, how much do 3 notebooks cost? (a) ₹47 (b) ₹144 (c) ₹36 (d) ₹48
7. 7.₹290 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹145 (b) ₹203 (c) ₹87 (d) ₹29
8. 8.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹200 (b) ₹40 (c) ₹240 (d) ₹220
9. 9.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 9 days (c) 4 days (d) 49 days
10. 10.If 7 mangoes cost ₹105, how much do 4 mangoes cost? (a) ₹75 (b) ₹60 (c) ₹102 (d) ₹420
11. 11.If 3 pens cost ₹39, how much do 8 pens cost? (a) ₹312 (b) ₹104 (c) ₹44 (d) ₹117
12. 12.₹344 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹172 (b) ₹215 (c) ₹43 (d) ₹129
13. 13.If 2 pens cost ₹36, how much do 8 pens cost? (a) ₹162 (b) ₹42 (c) ₹288 (d) ₹144
14. 14.If 5 kites cost ₹85, how much do 7 kites cost? (a) ₹119 (b) ₹136 (c) ₹87 (d) ₹595
15. 15.8 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 18 days (b) 10 days (c) 7 days (d) 28 days
16. 16.If 8 pens cost ₹192, how much do 11 pens cost? (a) ₹288 (b) ₹264 (c) ₹2112 (d) ₹195
17. 17.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 9 days (d) 8 days
18. 18.If 3 mangoes cost ₹51, how much do 6 mangoes cost? (a) ₹102 (b) ₹54 (c) ₹306 (d) ₹119
19. 19.₹198 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹198 (b) ₹22 (c) ₹99 (d) ₹176
20. 20.3 workers can build a wall in 12 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 18 days (c) 6 days (d) 36 days
21. 21.If 5 notebooks cost ₹30, how much do 2 notebooks cost? (a) ₹18 (b) ₹27 (c) ₹60 (d) ₹12
22. 22.9 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 1 day (c) 3 days (d) 7 days
23. 23.If 4 kites cost ₹72, how much do 11 kites cost? (a) ₹792 (b) ₹198 (c) ₹79 (d) ₹216
24. 24.If 4 notebooks cost ₹64, how much do 5 notebooks cost? (a) ₹96 (b) ₹80 (c) ₹320 (d) ₹65
25. 25.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 15 days (b) 20 days (c) 5 days (d) 6 days
26. 26.If 9 kites cost ₹144, how much do 5 kites cost? (a) ₹140 (b) ₹96 (c) ₹720 (d) ₹80
27. 27.₹120 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹20 (b) ₹60 (c) ₹120 (d) ₹100
28. 28.₹119 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹51 (b) ₹85 (c) ₹17 (d) ₹68
29. 29.If 4 mangoes cost ₹72, how much do 10 mangoes cost? (a) ₹180 (b) ₹198 (c) ₹720 (d) ₹78
30. 30.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 8 days (d) 10 days
31. 31.₹360 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹324 (b) ₹360 (c) ₹36 (d) ₹180
32. 32.₹121 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹33 (b) ₹88 (c) ₹11 (d) ₹99
33. 33.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 26 days (b) 27 days (c) 17 days (d) 9 days
34. 34.₹396 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹180 (b) ₹198 (c) ₹216 (d) ₹36
35. 35.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 4 days (d) 6 days
36. 36.If 3 mangoes cost ₹72, how much do 9 mangoes cost? (a) ₹648 (b) ₹78 (c) ₹240 (d) ₹216
37. 37.If 4 pens cost ₹32, how much do 7 pens cost? (a) ₹224 (b) ₹56 (c) ₹35 (d) ₹64
38. 38.₹171 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹152 (b) ₹19 (c) ₹133 (d) ₹38
39. 39.If 5 kites cost ₹15, how much do 11 kites cost? (a) ₹165 (b) ₹33 (c) ₹36 (d) ₹21
40. 40.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 11 days (d) 4 days

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