Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 503 · 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. 1.8 workers can build a wall in 9 days. How many days will 2 workers take, working at the same speed? (a) 37 days (b) 3 days (c) 36 days (d) 15 days
2. 2.4 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 11 days (c) 17 days (d) 9 days
3. 3.4 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 16 days (d) 12 days
4. 4.If 6 kites cost ₹120, how much do 12 kites cost? (a) ₹1440 (b) ₹126 (c) ₹260 (d) ₹240
5. 5.If 2 pens cost ₹44, how much do 5 pens cost? (a) ₹220 (b) ₹110 (c) ₹47 (d) ₹132
6. 6.₹88 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹55 (b) ₹44 (c) ₹11 (d) ₹33
7. 7.If 8 notebooks cost ₹136, how much do 11 notebooks cost? (a) ₹139 (b) ₹204 (c) ₹187 (d) ₹1496
8. 8.If 8 pens cost ₹136, how much do 12 pens cost? (a) ₹1632 (b) ₹140 (c) ₹204 (d) ₹221
9. 9.4 workers can build a wall in 6 days. How many days will 8 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 3 days (d) 10 days
10. 10.6 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 6 days (b) 7 days (c) 5 days (d) 8 days
11. 11.₹273 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹195 (b) ₹78 (c) ₹234 (d) ₹39
12. 12.If 2 mangoes cost ₹26, how much do 9 mangoes cost? (a) ₹117 (b) ₹234 (c) ₹130 (d) ₹33
13. 13.If 8 pens cost ₹192, how much do 5 pens cost? (a) ₹144 (b) ₹120 (c) ₹189 (d) ₹960
14. 14.If 6 pens cost ₹24, how much do 9 pens cost? (a) ₹216 (b) ₹36 (c) ₹27 (d) ₹40
15. 15.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 18 days (b) 43 days (c) 10 days (d) 42 days
16. 16.If 2 notebooks cost ₹14, how much do 6 notebooks cost? (a) ₹42 (b) ₹18 (c) ₹49 (d) ₹84
17. 17.4 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 14 days (b) 18 days (c) 8 days (d) 10 days
18. 18.If 5 mangoes cost ₹110, how much do 6 mangoes cost? (a) ₹154 (b) ₹132 (c) ₹111 (d) ₹660
19. 19.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹186 (b) ₹124 (c) ₹155 (d) ₹31
20. 20.4 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 14 days (c) 20 days (d) 16 days
21. 21.₹126 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹105 (b) ₹63 (c) ₹21 (d) ₹126
22. 22.If 9 kites cost ₹126, how much do 12 kites cost? (a) ₹168 (b) ₹182 (c) ₹1512 (d) ₹129
23. 23.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 21 days (b) 7 days (c) 6 days (d) 9 days
24. 24.If 4 notebooks cost ₹44, how much do 3 notebooks cost? (a) ₹33 (b) ₹43 (c) ₹44 (d) ₹132
25. 25.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 19 days (d) 2 days
26. 26.₹116 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹87 (b) ₹116 (c) ₹58 (d) ₹29
27. 27.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹18 (b) ₹24 (c) ₹36 (d) ₹12
28. 28.If 7 kites cost ₹154, how much do 9 kites cost? (a) ₹1386 (b) ₹198 (c) ₹220 (d) ₹156
29. 29.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 15 days (d) 22 days
30. 30.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 9 days
31. 31.If 2 kites cost ₹32, how much do 5 kites cost? (a) ₹35 (b) ₹160 (c) ₹96 (d) ₹80
32. 32.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 22 days (c) 1 day (d) 13 days
33. 33.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 44 days (b) 17 days (c) 5 days (d) 45 days
34. 34.If 5 notebooks cost ₹70, how much do 11 notebooks cost? (a) ₹770 (b) ₹168 (c) ₹154 (d) ₹76
35. 35.If 8 pens cost ₹192, how much do 9 pens cost? (a) ₹216 (b) ₹193 (c) ₹240 (d) ₹1728
36. 36.9 workers can build a wall in 12 days. How many days will 3 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 18 days (d) 36 days
37. 37.8 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 4 days (c) 12 days (d) 16 days
38. 38.If 3 pens cost ₹54, how much do 12 pens cost? (a) ₹234 (b) ₹63 (c) ₹216 (d) ₹648
39. 39.If 5 notebooks cost ₹40, how much do 6 notebooks cost? (a) ₹240 (b) ₹41 (c) ₹56 (d) ₹48
40. 40.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 19 days (b) 3 days (c) 4 days (d) 2 days

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