Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 465 · 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 9 pens cost ₹153, how much do 4 pens cost? (a) ₹612 (b) ₹148 (c) ₹85 (d) ₹68
2. 2.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹288 (b) ₹240 (c) ₹336 (d) ₹48
3. 3.₹216 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹48 (b) ₹24 (c) ₹168 (d) ₹108
4. 4.If 5 pens cost ₹50, how much do 6 pens cost? (a) ₹60 (b) ₹300 (c) ₹70 (d) ₹51
5. 5.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 2 days (c) 11 days (d) 3 days
6. 6.₹56 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹56 (b) ₹7 (c) ₹28 (d) ₹49
7. 7.If 9 pens cost ₹180, how much do 10 pens cost? (a) ₹200 (b) ₹181 (c) ₹220 (d) ₹1800
8. 8.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 6 days
9. 9.₹396 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹88 (b) ₹308 (c) ₹198 (d) ₹44
10. 10.9 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 54 days (b) 55 days (c) 19 days (d) 5 days
11. 11.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 12 days (c) 20 days (d) 8 days
12. 12.6 workers can build a wall in 4 days. How many days will 3 workers take, working at the same speed? (a) 1 day (b) 7 days (c) 8 days (d) 2 days
13. 13.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 23 days (c) 13 days (d) 22 days
14. 14.If 8 kites cost ₹48, how much do 6 kites cost? (a) ₹288 (b) ₹42 (c) ₹46 (d) ₹36
15. 15.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 9 days (d) 25 days
16. 16.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 28 days (d) 7 days
17. 17.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 13 days (c) 7 days (d) 12 days
18. 18.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 28 days (c) 3 days (d) 27 days
19. 19.If 4 pens cost ₹32, how much do 5 pens cost? (a) ₹40 (b) ₹160 (c) ₹33 (d) ₹48
20. 20.If 9 pens cost ₹99, how much do 4 pens cost? (a) ₹55 (b) ₹44 (c) ₹396 (d) ₹94
21. 21.If 2 kites cost ₹28, how much do 3 kites cost? (a) ₹84 (b) ₹42 (c) ₹29 (d) ₹56
22. 22.₹110 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹10 (b) ₹70 (c) ₹55 (d) ₹40
23. 23.8 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 7 days (b) 9 days (c) 2 days (d) 8 days
24. 24.₹616 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹308 (b) ₹44 (c) ₹396 (d) ₹220
25. 25.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 15 days (c) 5 days (d) 20 days
26. 26.If 8 pens cost ₹176, how much do 7 pens cost? (a) ₹1232 (b) ₹176 (c) ₹175 (d) ₹154
27. 27.5 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 36 days (c) 35 days (d) 11 days
28. 28.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹162 (b) ₹27 (c) ₹108 (d) ₹135
29. 29.If 6 pens cost ₹114, how much do 10 pens cost? (a) ₹190 (b) ₹209 (c) ₹118 (d) ₹1140
30. 30.₹539 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹343 (b) ₹196 (c) ₹49 (d) ₹392
31. 31.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 5 days (d) 3 days
32. 32.₹598 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹184 (b) ₹299 (c) ₹46 (d) ₹414
33. 33.If 2 notebooks cost ₹14, how much do 3 notebooks cost? (a) ₹42 (b) ₹15 (c) ₹28 (d) ₹21
34. 34.If 2 notebooks cost ₹28, how much do 6 notebooks cost? (a) ₹168 (b) ₹32 (c) ₹98 (d) ₹84
35. 35.₹336 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹168 (b) ₹144 (c) ₹48 (d) ₹192
36. 36.If 3 pens cost ₹57, how much do 4 pens cost? (a) ₹58 (b) ₹76 (c) ₹228 (d) ₹95
37. 37.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 6 days (d) 16 days
38. 38.If 8 kites cost ₹120, how much do 11 kites cost? (a) ₹123 (b) ₹180 (c) ₹165 (d) ₹1320
39. 39.₹54 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹27 (b) ₹36 (c) ₹18 (d) ₹54
40. 40.8 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 48 days (c) 18 days (d) 6 days

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