Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 520 · 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 9 pens cost ₹171, how much do 10 pens cost? (a) ₹190 (b) ₹209 (c) ₹172 (d) ₹1710
2. 2.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹35 (b) ₹7 (c) ₹49 (d) ₹63
3. 3.If 7 kites cost ₹42, how much do 4 kites cost? (a) ₹30 (b) ₹168 (c) ₹39 (d) ₹24
4. 4.If 5 notebooks cost ₹65, how much do 2 notebooks cost? (a) ₹26 (b) ₹39 (c) ₹62 (d) ₹130
5. 5.₹380 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹38 (b) ₹114 (c) ₹266 (d) ₹190
6. 6.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 17 days (d) 11 days
7. 7.If 6 pens cost ₹84, how much do 9 pens cost? (a) ₹140 (b) ₹756 (c) ₹87 (d) ₹126
8. 8.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 13 days (c) 2 days (d) 3 days
9. 9.If 2 pens cost ₹22, how much do 8 pens cost? (a) ₹99 (b) ₹28 (c) ₹176 (d) ₹88
10. 10.8 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 8 days (d) 4 days
11. 11.8 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 8 days (b) 12 days (c) 9 days (d) 7 days
12. 12.₹187 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹153 (b) ₹51 (c) ₹17 (d) ₹136
13. 13.If 3 kites cost ₹66, how much do 8 kites cost? (a) ₹198 (b) ₹176 (c) ₹71 (d) ₹528
14. 14.₹161 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹138 (b) ₹161 (c) ₹23 (d) ₹139
15. 15.₹154 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹11 (b) ₹77 (c) ₹99 (d) ₹55
16. 16.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 44 days (b) 17 days (c) 45 days (d) 5 days
17. 17.5 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) 4 days (d) 9 days
18. 18.If 6 notebooks cost ₹126, how much do 3 notebooks cost? (a) ₹63 (b) ₹378 (c) ₹123 (d) ₹84
19. 19.If 6 pens cost ₹36, how much do 7 pens cost? (a) ₹42 (b) ₹37 (c) ₹48 (d) ₹252
20. 20.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 7 days (d) 12 days
21. 21.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 21 days (c) 22 days (d) 5 days
22. 22.If 7 kites cost ₹168, how much do 5 kites cost? (a) ₹166 (b) ₹120 (c) ₹144 (d) ₹840
23. 23.If 2 mangoes cost ₹44, how much do 6 mangoes cost? (a) ₹154 (b) ₹48 (c) ₹264 (d) ₹132
24. 24.₹220 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹100 (b) ₹110 (c) ₹20 (d) ₹120
25. 25.₹242 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹22 (b) ₹121 (c) ₹44 (d) ₹198
26. 26.₹572 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹176 (b) ₹286 (c) ₹396 (d) ₹44
27. 27.If 6 pens cost ₹102, how much do 10 pens cost? (a) ₹1020 (b) ₹170 (c) ₹187 (d) ₹106
28. 28.If 5 pens cost ₹70, how much do 2 pens cost? (a) ₹140 (b) ₹42 (c) ₹28 (d) ₹67
29. 29.₹312 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹192 (b) ₹156 (c) ₹120 (d) ₹24
30. 30.₹396 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹165 (b) ₹231 (c) ₹33 (d) ₹198
31. 31.If 5 kites cost ₹100, how much do 11 kites cost? (a) ₹220 (b) ₹106 (c) ₹1100 (d) ₹240
32. 32.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 28 days (b) 19 days (c) 7 days (d) 9 days
33. 33.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 7 days
34. 34.9 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 14 days (c) 11 days (d) 15 days
35. 35.₹60 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹24 (b) ₹30 (c) ₹12 (d) ₹36
36. 36.If 2 mangoes cost ₹24, how much do 4 mangoes cost? (a) ₹48 (b) ₹26 (c) ₹60 (d) ₹96
37. 37.If 3 kites cost ₹33, how much do 9 kites cost? (a) ₹110 (b) ₹99 (c) ₹297 (d) ₹39
38. 38.If 5 pens cost ₹75, how much do 10 pens cost? (a) ₹80 (b) ₹165 (c) ₹750 (d) ₹150
39. 39.If 4 notebooks cost ₹44, how much do 3 notebooks cost? (a) ₹132 (b) ₹33 (c) ₹44 (d) ₹43
40. 40.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 7 days (d) 6 days

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