Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 166 · 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 7 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 9 days (c) 14 days (d) 5 days
2. 2.₹539 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹147 (b) ₹49 (c) ₹441 (d) ₹392
3. 3.If 8 notebooks cost ₹136, how much do 7 notebooks cost? (a) ₹952 (b) ₹135 (c) ₹136 (d) ₹119
4. 4.5 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 19 days
5. 5.₹180 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹90 (b) ₹15 (c) ₹105 (d) ₹75
6. 6.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 9 days (d) 2 days
7. 7.7 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) 15 days (d) 14 days
8. 8.If 2 kites cost ₹50, how much do 4 kites cost? (a) ₹200 (b) ₹125 (c) ₹100 (d) ₹52
9. 9.7 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 7 days (d) 8 days
10. 10.₹88 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹44 (b) ₹8 (c) ₹24 (d) ₹64
11. 11.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 11 days (d) 3 days
12. 12.If 6 pens cost ₹54, how much do 12 pens cost? (a) ₹60 (b) ₹648 (c) ₹117 (d) ₹108
13. 13.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 18 days (c) 4 days (d) 3 days
14. 14.₹90 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹45 (b) ₹75 (c) ₹90 (d) ₹15
15. 15.6 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 13 days (d) 12 days
16. 16.If 6 kites cost ₹54, how much do 7 kites cost? (a) ₹378 (b) ₹55 (c) ₹63 (d) ₹72
17. 17.If 6 notebooks cost ₹132, how much do 8 notebooks cost? (a) ₹176 (b) ₹198 (c) ₹1056 (d) ₹134
18. 18.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 15 days (c) 6 days (d) 5 days
19. 19.₹315 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹35 (b) ₹315 (c) ₹281 (d) ₹280
20. 20.If 8 mangoes cost ₹112, how much do 3 mangoes cost? (a) ₹336 (b) ₹42 (c) ₹56 (d) ₹107
21. 21.₹208 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹78 (b) ₹104 (c) ₹26 (d) ₹130
22. 22.If 3 pens cost ₹30, how much do 9 pens cost? (a) ₹100 (b) ₹90 (c) ₹270 (d) ₹36
23. 23.If 5 mangoes cost ₹60, how much do 11 mangoes cost? (a) ₹132 (b) ₹660 (c) ₹144 (d) ₹66
24. 24.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 6 days
25. 25.3 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 4 days (d) 9 days
26. 26.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 16 days (c) 4 days (d) 12 days
27. 27.If 5 notebooks cost ₹35, how much do 6 notebooks cost? (a) ₹36 (b) ₹42 (c) ₹210 (d) ₹49
28. 28.If 5 notebooks cost ₹125, how much do 11 notebooks cost? (a) ₹131 (b) ₹300 (c) ₹275 (d) ₹1375
29. 29.If 5 notebooks cost ₹85, how much do 6 notebooks cost? (a) ₹102 (b) ₹510 (c) ₹86 (d) ₹119
30. 30.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 1 day (c) 11 days (d) 17 days
31. 31.If 6 notebooks cost ₹36, how much do 2 notebooks cost? (a) ₹12 (b) ₹18 (c) ₹72 (d) ₹32
32. 32.If 4 kites cost ₹96, how much do 10 kites cost? (a) ₹264 (b) ₹240 (c) ₹960 (d) ₹102
33. 33.₹330 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹165 (b) ₹180 (c) ₹150 (d) ₹30
34. 34.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 10 days (c) 4 days (d) 15 days
35. 35.If 8 notebooks cost ₹200, how much do 6 notebooks cost? (a) ₹1200 (b) ₹175 (c) ₹198 (d) ₹150
36. 36.₹217 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹155 (b) ₹62 (c) ₹186 (d) ₹31
37. 37.₹451 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹328 (b) ₹164 (c) ₹287 (d) ₹41
38. 38.₹54 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹30 (b) ₹6 (c) ₹24 (d) ₹27
39. 39.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹43 (b) ₹129 (c) ₹87 (d) ₹86
40. 40.If 8 mangoes cost ₹176, how much do 3 mangoes cost? (a) ₹88 (b) ₹528 (c) ₹171 (d) ₹66

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