Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 171 · 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. 1.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 5 days (d) 12 days
2. 2.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 43 days (b) 42 days (c) 18 days (d) 10 days
3. 3.₹180 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹90 (b) ₹126 (c) ₹54 (d) ₹18
4. 4.₹494 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹152 (b) ₹38 (c) ₹342 (d) ₹247
5. 5.₹455 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹315 (b) ₹35 (c) ₹140 (d) ₹350
6. 6.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 12 days (c) 25 days (d) 23 days
7. 7.₹247 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹171 (b) ₹95 (c) ₹19 (d) ₹152
8. 8.₹253 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹23 (b) ₹161 (c) ₹184 (d) ₹92
9. 9.If 5 pens cost ₹15, how much do 3 pens cost? (a) ₹13 (b) ₹45 (c) ₹9 (d) ₹12
10. 10.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹92 (b) ₹69 (c) ₹115 (d) ₹23
11. 11.₹192 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹48 (b) ₹96 (c) ₹192 (d) ₹144
12. 12.If 7 mangoes cost ₹98, how much do 8 mangoes cost? (a) ₹784 (b) ₹99 (c) ₹112 (d) ₹126
13. 13.If 3 mangoes cost ₹60, how much do 2 mangoes cost? (a) ₹40 (b) ₹60 (c) ₹120 (d) ₹59
14. 14.If 4 notebooks cost ₹92, how much do 2 notebooks cost? (a) ₹46 (b) ₹69 (c) ₹184 (d) ₹90
15. 15.5 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 20 days (d) 11 days
16. 16.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 15 days (b) 12 days (c) 8 days (d) 14 days
17. 17.₹572 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹220 (b) ₹44 (c) ₹352 (d) ₹286
18. 18.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 11 days (d) 16 days
19. 19.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 3 days (d) 7 days
20. 20.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 11 days (d) 15 days
21. 21.If 3 pens cost ₹30, how much do 8 pens cost? (a) ₹240 (b) ₹35 (c) ₹80 (d) ₹90
22. 22.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 4 days (b) 16 days (c) 12 days (d) 17 days
23. 23.If 9 pens cost ₹99, how much do 7 pens cost? (a) ₹97 (b) ₹693 (c) ₹88 (d) ₹77
24. 24.₹27 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹9 (b) ₹18 (c) ₹19 (d) ₹27
25. 25.₹248 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹124 (b) ₹155 (c) ₹31 (d) ₹93
26. 26.4 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 5 days (d) 14 days
27. 27.If 5 kites cost ₹85, how much do 6 kites cost? (a) ₹510 (b) ₹86 (c) ₹119 (d) ₹102
28. 28.If 2 mangoes cost ₹6, how much do 11 mangoes cost? (a) ₹15 (b) ₹66 (c) ₹36 (d) ₹33
29. 29.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 8 days
30. 30.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 8 days (d) 12 days
31. 31.If 3 notebooks cost ₹45, how much do 4 notebooks cost? (a) ₹46 (b) ₹60 (c) ₹75 (d) ₹180
32. 32.If 4 mangoes cost ₹80, how much do 5 mangoes cost? (a) ₹400 (b) ₹120 (c) ₹81 (d) ₹100
33. 33.₹392 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹140 (b) ₹28 (c) ₹196 (d) ₹252
34. 34.If 9 pens cost ₹135, how much do 11 pens cost? (a) ₹137 (b) ₹1485 (c) ₹180 (d) ₹165
35. 35.₹162 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹81 (b) ₹162 (c) ₹18 (d) ₹144
36. 36.₹99 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹11 (b) ₹88 (c) ₹77 (d) ₹22
37. 37.If 5 mangoes cost ₹50, how much do 6 mangoes cost? (a) ₹51 (b) ₹70 (c) ₹60 (d) ₹300
38. 38.If 8 mangoes cost ₹168, how much do 3 mangoes cost? (a) ₹84 (b) ₹163 (c) ₹63 (d) ₹504
39. 39.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 26 days (c) 27 days (d) 13 days
40. 40.₹88 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹44 (b) ₹40 (c) ₹8 (d) ₹48

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