Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 414 · 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 8 mangoes cost ₹24, how much do 10 mangoes cost? (a) ₹30 (b) ₹240 (c) ₹26 (d) ₹33
2. 2.If 3 notebooks cost ₹69, how much do 11 notebooks cost? (a) ₹77 (b) ₹276 (c) ₹253 (d) ₹759
3. 3.9 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 43 days (b) 8 days (c) 20 days (d) 42 days
4. 4.₹270 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹210 (b) ₹135 (c) ₹60 (d) ₹30
5. 5.If 5 notebooks cost ₹45, how much do 10 notebooks cost? (a) ₹450 (b) ₹50 (c) ₹99 (d) ₹90
6. 6.₹338 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹130 (b) ₹169 (c) ₹208 (d) ₹26
7. 7.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹78 (b) ₹52 (c) ₹26 (d) ₹39
8. 8.If 7 notebooks cost ₹168, how much do 4 notebooks cost? (a) ₹672 (b) ₹96 (c) ₹165 (d) ₹120
9. 9.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 7 days (d) 9 days
10. 10.₹306 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹34 (b) ₹306 (c) ₹272 (d) ₹153
11. 11.4 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 12 days (d) 10 days
12. 12.3 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
13. 13.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 17 days (d) 4 days
14. 14.If 3 notebooks cost ₹36, how much do 4 notebooks cost? (a) ₹48 (b) ₹37 (c) ₹60 (d) ₹144
15. 15.4 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 10 days (d) 4 days
16. 16.₹220 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹110 (b) ₹132 (c) ₹44 (d) ₹88
17. 17.If 3 mangoes cost ₹36, how much do 4 mangoes cost? (a) ₹60 (b) ₹144 (c) ₹48 (d) ₹37
18. 18.If 4 mangoes cost ₹52, how much do 3 mangoes cost? (a) ₹156 (b) ₹52 (c) ₹39 (d) ₹51
19. 19.If 3 notebooks cost ₹33, how much do 4 notebooks cost? (a) ₹55 (b) ₹132 (c) ₹44 (d) ₹34
20. 20.If 2 mangoes cost ₹30, how much do 12 mangoes cost? (a) ₹195 (b) ₹40 (c) ₹180 (d) ₹360
21. 21.If 7 kites cost ₹154, how much do 8 kites cost? (a) ₹155 (b) ₹176 (c) ₹198 (d) ₹1232
22. 22.If 2 notebooks cost ₹30, how much do 8 notebooks cost? (a) ₹36 (b) ₹120 (c) ₹135 (d) ₹240
23. 23.₹99 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹45 (b) ₹54 (c) ₹63 (d) ₹9
24. 24.₹248 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹124 (b) ₹31 (c) ₹155 (d) ₹93
25. 25.If 6 pens cost ₹126, how much do 2 pens cost? (a) ₹122 (b) ₹63 (c) ₹42 (d) ₹252
26. 26.6 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 5 days (d) 14 days
27. 27.4 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 7 days (c) 3 days (d) 10 days
28. 28.3 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 24 days (b) 9 days (c) 6 days (d) 15 days
29. 29.₹559 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹387 (b) ₹430 (c) ₹43 (d) ₹172
30. 30.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 9 days (d) 21 days
31. 31.6 workers can build a wall in 14 days. How many days will 4 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 16 days (d) 12 days
32. 32.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 4 days (c) 2 days (d) 3 days
33. 33.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 3 days (d) 18 days
34. 34.If 7 notebooks cost ₹84, how much do 11 notebooks cost? (a) ₹132 (b) ₹144 (c) ₹924 (d) ₹88
35. 35.If 6 pens cost ₹60, how much do 3 pens cost? (a) ₹40 (b) ₹30 (c) ₹180 (d) ₹57
36. 36.If 7 pens cost ₹168, how much do 8 pens cost? (a) ₹1344 (b) ₹216 (c) ₹192 (d) ₹169
37. 37.If 3 mangoes cost ₹75, how much do 5 mangoes cost? (a) ₹150 (b) ₹77 (c) ₹375 (d) ₹125
38. 38.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 27 days (d) 4 days
39. 39.If 4 pens cost ₹68, how much do 5 pens cost? (a) ₹102 (b) ₹69 (c) ₹85 (d) ₹340
40. 40.₹473 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹301 (b) ₹215 (c) ₹258 (d) ₹43

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