Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 645 · 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.₹120 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹60 (b) ₹45 (c) ₹75 (d) ₹15
2. 2.₹105 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹91 (b) ₹15 (c) ₹105 (d) ₹90
3. 3.If 2 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹29 (b) ₹42 (c) ₹84 (d) ₹56
4. 4.₹342 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹38 (b) ₹190 (c) ₹152 (d) ₹171
5. 5.If 2 pens cost ₹44, how much do 9 pens cost? (a) ₹220 (b) ₹396 (c) ₹198 (d) ₹51
6. 6.If 5 kites cost ₹30, how much do 6 kites cost? (a) ₹180 (b) ₹36 (c) ₹42 (d) ₹31
7. 7.If 5 pens cost ₹120, how much do 2 pens cost? (a) ₹72 (b) ₹48 (c) ₹240 (d) ₹117
8. 8.If 4 kites cost ₹36, how much do 5 kites cost? (a) ₹37 (b) ₹54 (c) ₹180 (d) ₹45
9. 9.If 7 pens cost ₹112, how much do 4 pens cost? (a) ₹64 (b) ₹80 (c) ₹109 (d) ₹448
10. 10.₹232 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹232 (b) ₹116 (c) ₹29 (d) ₹203
11. 11.₹403 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹31 (b) ₹248 (c) ₹279 (d) ₹155
12. 12.If 4 notebooks cost ₹40, how much do 6 notebooks cost? (a) ₹42 (b) ₹60 (c) ₹240 (d) ₹70
13. 13.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 8 days (b) 3 days (c) 1 day (d) 2 days
14. 14.₹80 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹10 (b) ₹40 (c) ₹50 (d) ₹30
15. 15.If 4 kites cost ₹92, how much do 6 kites cost? (a) ₹161 (b) ₹94 (c) ₹552 (d) ₹138
16. 16.₹160 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹60 (b) ₹80 (c) ₹100 (d) ₹20
17. 17.If 6 notebooks cost ₹66, how much do 7 notebooks cost? (a) ₹462 (b) ₹77 (c) ₹88 (d) ₹67
18. 18.If 2 mangoes cost ₹30, how much do 11 mangoes cost? (a) ₹165 (b) ₹180 (c) ₹39 (d) ₹330
19. 19.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 9 days (b) 4 days (c) 2 days (d) 10 days
20. 20.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 8 days (c) 6 days (d) 7 days
21. 21.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 11 days
22. 22.If 9 notebooks cost ₹99, how much do 4 notebooks cost? (a) ₹396 (b) ₹44 (c) ₹94 (d) ₹55
23. 23.If 3 mangoes cost ₹33, how much do 4 mangoes cost? (a) ₹44 (b) ₹55 (c) ₹132 (d) ₹34
24. 24.If 7 notebooks cost ₹119, how much do 2 notebooks cost? (a) ₹238 (b) ₹51 (c) ₹114 (d) ₹34
25. 25.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 45 days (d) 9 days
26. 26.6 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) 25 days (d) 24 days
27. 27.₹374 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹102 (b) ₹187 (c) ₹34 (d) ₹272
28. 28.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 7 days (d) 9 days
29. 29.₹240 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹240 (b) ₹40 (c) ₹120 (d) ₹200
30. 30.If 2 mangoes cost ₹26, how much do 5 mangoes cost? (a) ₹78 (b) ₹65 (c) ₹29 (d) ₹130
31. 31.If 6 notebooks cost ₹120, how much do 5 notebooks cost? (a) ₹119 (b) ₹600 (c) ₹120 (d) ₹100
32. 32.₹200 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹25 (b) ₹125 (c) ₹100 (d) ₹75
33. 33.If 2 notebooks cost ₹22, how much do 3 notebooks cost? (a) ₹33 (b) ₹44 (c) ₹23 (d) ₹66
34. 34.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 5 days (d) 15 days
35. 35.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 15 days (d) 14 days
36. 36.If 8 notebooks cost ₹64, how much do 3 notebooks cost? (a) ₹192 (b) ₹24 (c) ₹59 (d) ₹32
37. 37.If 4 kites cost ₹72, how much do 2 kites cost? (a) ₹144 (b) ₹70 (c) ₹54 (d) ₹36
38. 38.7 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
39. 39.₹225 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹180 (b) ₹90 (c) ₹135 (d) ₹45
40. 40.If 3 kites cost ₹42, how much do 4 kites cost? (a) ₹70 (b) ₹56 (c) ₹43 (d) ₹168

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