Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 700 · 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. 1.9 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 39 days (b) 40 days (c) 7 days (d) 19 days
2. 2.If 3 mangoes cost ₹42, how much do 11 mangoes cost? (a) ₹154 (b) ₹50 (c) ₹462 (d) ₹168
3. 3.9 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
4. 4.If 7 pens cost ₹119, how much do 4 pens cost? (a) ₹68 (b) ₹116 (c) ₹476 (d) ₹85
5. 5.If 7 pens cost ₹42, how much do 3 pens cost? (a) ₹18 (b) ₹24 (c) ₹126 (d) ₹38
6. 6.₹230 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹23 (b) ₹207 (c) ₹115 (d) ₹230
7. 7.7 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
8. 8.₹144 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹144 (b) ₹36 (c) ₹108 (d) ₹72
9. 9.If 6 pens cost ₹114, how much do 10 pens cost? (a) ₹209 (b) ₹1140 (c) ₹118 (d) ₹190
10. 10.₹410 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹41 (b) ₹410 (c) ₹369 (d) ₹205
11. 11.If 8 notebooks cost ₹56, how much do 5 notebooks cost? (a) ₹53 (b) ₹280 (c) ₹42 (d) ₹35
12. 12.₹348 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹174 (b) ₹29 (c) ₹203 (d) ₹145
13. 13.If 8 kites cost ₹72, how much do 12 kites cost? (a) ₹864 (b) ₹76 (c) ₹108 (d) ₹117
14. 14.₹52 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹13 (b) ₹39 (c) ₹52 (d) ₹26
15. 15.₹280 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹80 (b) ₹140 (c) ₹40 (d) ₹200
16. 16.₹473 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹430 (b) ₹43 (c) ₹86 (d) ₹387
17. 17.If 8 pens cost ₹104, how much do 4 pens cost? (a) ₹52 (b) ₹100 (c) ₹416 (d) ₹65
18. 18.₹48 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹24 (b) ₹6 (c) ₹18 (d) ₹30
19. 19.₹190 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹95 (b) ₹38 (c) ₹114 (d) ₹76
20. 20.If 9 pens cost ₹135, how much do 11 pens cost? (a) ₹1485 (b) ₹180 (c) ₹165 (d) ₹137
21. 21.If 4 mangoes cost ₹16, how much do 12 mangoes cost? (a) ₹192 (b) ₹52 (c) ₹48 (d) ₹24
22. 22.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹50 (b) ₹10 (c) ₹30 (d) ₹70
23. 23.If 2 kites cost ₹14, how much do 7 kites cost? (a) ₹19 (b) ₹98 (c) ₹49 (d) ₹56
24. 24.₹441 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹392 (b) ₹393 (c) ₹441 (d) ₹49
25. 25.If 6 kites cost ₹126, how much do 12 kites cost? (a) ₹132 (b) ₹252 (c) ₹1512 (d) ₹273
26. 26.₹238 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹34 (b) ₹119 (c) ₹136 (d) ₹102
27. 27.If 2 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹42 (b) ₹84 (c) ₹56 (d) ₹29
28. 28.6 workers can build a wall in 10 days. How many days will 3 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 20 days (d) 5 days
29. 29.8 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 8 days (c) 9 days (d) 7 days
30. 30.If 6 pens cost ₹120, how much do 2 pens cost? (a) ₹40 (b) ₹240 (c) ₹116 (d) ₹60
31. 31.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 18 days (c) 12 days (d) 2 days
32. 32.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹92 (b) ₹115 (c) ₹46 (d) ₹138
33. 33.If 2 kites cost ₹34, how much do 11 kites cost? (a) ₹374 (b) ₹187 (c) ₹43 (d) ₹204
34. 34.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 17 days (d) 2 days
35. 35.If 4 kites cost ₹52, how much do 7 kites cost? (a) ₹55 (b) ₹364 (c) ₹104 (d) ₹91
36. 36.3 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 27 days (b) 3 days (c) 4 days (d) 15 days
37. 37.If 6 mangoes cost ₹108, how much do 11 mangoes cost? (a) ₹1188 (b) ₹113 (c) ₹216 (d) ₹198
38. 38.₹517 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹94 (b) ₹423 (c) ₹47 (d) ₹470
39. 39.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 49 days (c) 4 days (d) 19 days
40. 40.₹66 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹33 (b) ₹6 (c) ₹36 (d) ₹30

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