Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 213 · 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 ₹54, how much do 4 pens cost? (a) ₹49 (b) ₹216 (c) ₹30 (d) ₹24
2. 2.If 5 notebooks cost ₹25, how much do 11 notebooks cost? (a) ₹275 (b) ₹31 (c) ₹60 (d) ₹55
3. 3.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 27 days (c) 26 days (d) 13 days
4. 4.If 9 mangoes cost ₹162, how much do 6 mangoes cost? (a) ₹108 (b) ₹159 (c) ₹972 (d) ₹126
5. 5.₹64 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹8 (b) ₹56 (c) ₹64 (d) ₹32
6. 6.If 3 notebooks cost ₹48, how much do 11 notebooks cost? (a) ₹192 (b) ₹176 (c) ₹56 (d) ₹528
7. 7.If 8 pens cost ₹104, how much do 7 pens cost? (a) ₹103 (b) ₹728 (c) ₹104 (d) ₹91
8. 8.If 5 pens cost ₹75, how much do 8 pens cost? (a) ₹78 (b) ₹120 (c) ₹600 (d) ₹135
9. 9.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 9 days
10. 10.₹77 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹33 (b) ₹11 (c) ₹44 (d) ₹55
11. 11.If 9 pens cost ₹198, how much do 10 pens cost? (a) ₹220 (b) ₹242 (c) ₹1980 (d) ₹199
12. 12.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 19 days (c) 2 days (d) 4 days
13. 13.If 2 pens cost ₹34, how much do 11 pens cost? (a) ₹43 (b) ₹204 (c) ₹187 (d) ₹374
14. 14.If 2 mangoes cost ₹24, how much do 3 mangoes cost? (a) ₹36 (b) ₹48 (c) ₹25 (d) ₹72
15. 15.If 2 kites cost ₹34, how much do 4 kites cost? (a) ₹85 (b) ₹136 (c) ₹68 (d) ₹36
16. 16.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 8 days (c) 17 days (d) 11 days
17. 17.If 9 pens cost ₹63, how much do 10 pens cost? (a) ₹77 (b) ₹64 (c) ₹630 (d) ₹70
18. 18.If 7 kites cost ₹147, how much do 9 kites cost? (a) ₹149 (b) ₹210 (c) ₹1323 (d) ₹189
19. 19.If 6 notebooks cost ₹102, how much do 8 notebooks cost? (a) ₹136 (b) ₹816 (c) ₹153 (d) ₹104
20. 20.If 4 kites cost ₹40, how much do 10 kites cost? (a) ₹110 (b) ₹100 (c) ₹46 (d) ₹400
21. 21.If 2 pens cost ₹44, how much do 12 pens cost? (a) ₹54 (b) ₹264 (c) ₹286 (d) ₹528
22. 22.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 5 days (d) 20 days
23. 23.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 11 days (d) 8 days
24. 24.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 4 days (d) 49 days
25. 25.7 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 5 days (d) 7 days
26. 26.₹165 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹132 (b) ₹66 (c) ₹33 (d) ₹99
27. 27.7 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 1 day (d) 7 days
28. 28.If 2 pens cost ₹12, how much do 3 pens cost? (a) ₹13 (b) ₹24 (c) ₹18 (d) ₹36
29. 29.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 14 days (c) 15 days (d) 11 days
30. 30.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 10 days (d) 12 days
31. 31.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹120 (b) ₹15 (c) ₹30 (d) ₹105
32. 32.If 8 pens cost ₹112, how much do 11 pens cost? (a) ₹1232 (b) ₹154 (c) ₹115 (d) ₹168
33. 33.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 11 days (b) 2 days (c) 4 days (d) 3 days
34. 34.If 6 notebooks cost ₹132, how much do 2 notebooks cost? (a) ₹128 (b) ₹66 (c) ₹264 (d) ₹44
35. 35.5 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 3 days
36. 36.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 6 days (c) 36 days (d) 4 days
37. 37.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 3 days (d) 7 days
38. 38.₹230 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹115 (b) ₹230 (c) ₹23 (d) ₹207
39. 39.8 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 4 days (d) 5 days
40. 40.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹27 (b) ₹162 (c) ₹108 (d) ₹135

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