Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 2 · 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 7 kites cost ₹77, how much do 10 kites cost? (a) ₹110 (b) ₹80 (c) ₹121 (d) ₹770
2. 2.₹180 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹40 (b) ₹20 (c) ₹90 (d) ₹140
3. 3.₹252 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹56 (b) ₹196 (c) ₹28 (d) ₹126
4. 4.₹30 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹20 (b) ₹10 (c) ₹30 (d) ₹15
5. 5.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 7 days (c) 6 days (d) 3 days
6. 6.If 6 mangoes cost ₹150, how much do 9 mangoes cost? (a) ₹1350 (b) ₹250 (c) ₹225 (d) ₹153
7. 7.4 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 14 days (c) 12 days (d) 16 days
8. 8.9 workers can build a wall in 10 days. How many days will 6 workers take, working at the same speed? (a) 15 days (b) 13 days (c) 7 days (d) 16 days
9. 9.8 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 17 days (d) 16 days
10. 10.₹259 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹148 (b) ₹185 (c) ₹111 (d) ₹37
11. 11.If 5 pens cost ₹15, how much do 3 pens cost? (a) ₹45 (b) ₹9 (c) ₹13 (d) ₹12
12. 12.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 16 days (c) 7 days (d) 12 days
13. 13.If 8 pens cost ₹176, how much do 7 pens cost? (a) ₹176 (b) ₹154 (c) ₹175 (d) ₹1232
14. 14.4 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) 12 days (d) 5 days
15. 15.If 9 mangoes cost ₹108, how much do 12 mangoes cost? (a) ₹1296 (b) ₹111 (c) ₹144 (d) ₹156
16. 16.If 4 notebooks cost ₹28, how much do 3 notebooks cost? (a) ₹27 (b) ₹84 (c) ₹21 (d) ₹28
17. 17.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 7 days (c) 18 days (d) 6 days
18. 18.If 9 pens cost ₹216, how much do 12 pens cost? (a) ₹2592 (b) ₹288 (c) ₹219 (d) ₹312
19. 19.₹221 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹17 (b) ₹153 (c) ₹85 (d) ₹136
20. 20.₹234 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹26 (b) ₹117 (c) ₹104 (d) ₹130
21. 21.If 5 kites cost ₹30, how much do 10 kites cost? (a) ₹35 (b) ₹300 (c) ₹66 (d) ₹60
22. 22.If 7 pens cost ₹119, how much do 6 pens cost? (a) ₹102 (b) ₹119 (c) ₹118 (d) ₹714
23. 23.If 3 pens cost ₹72, how much do 6 pens cost? (a) ₹432 (b) ₹144 (c) ₹168 (d) ₹75
24. 24.If 6 kites cost ₹90, how much do 2 kites cost? (a) ₹45 (b) ₹86 (c) ₹30 (d) ₹180
25. 25.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 7 days (d) 3 days
26. 26.8 workers can build a wall in 7 days. How many days will 4 workers take, working at the same speed? (a) 3 days (b) 15 days (c) 11 days (d) 14 days
27. 27.If 9 notebooks cost ₹171, how much do 3 notebooks cost? (a) ₹57 (b) ₹165 (c) ₹513 (d) ₹76
28. 28.8 workers can build a wall in 5 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 11 days (c) 21 days (d) 20 days
29. 29.8 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 17 days (b) 13 days (c) 11 days (d) 12 days
30. 30.7 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 3 days (c) 8 days (d) 6 days
31. 31.If 8 notebooks cost ₹144, how much do 2 notebooks cost? (a) ₹54 (b) ₹288 (c) ₹138 (d) ₹36
32. 32.₹368 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹46 (b) ₹138 (c) ₹230 (d) ₹184
33. 33.If 9 mangoes cost ₹27, how much do 8 mangoes cost? (a) ₹26 (b) ₹24 (c) ₹216 (d) ₹27
34. 34.3 workers can build a wall in 15 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 21 days (c) 45 days (d) 9 days
35. 35.If 6 kites cost ₹114, how much do 7 kites cost? (a) ₹115 (b) ₹798 (c) ₹152 (d) ₹133
36. 36.₹369 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹328 (b) ₹41 (c) ₹287 (d) ₹82
37. 37.₹588 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹49 (b) ₹294 (c) ₹343 (d) ₹245
38. 38.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 2 days (b) 1 day (c) 13 days (d) 16 days
39. 39.3 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 18 days (b) 3 days (c) 12 days (d) 2 days
40. 40.8 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 9 days (d) 14 days

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