Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 479 · 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 2 notebooks cost ₹16, how much do 11 notebooks cost? (a) ₹25 (b) ₹96 (c) ₹176 (d) ₹88
2. 2.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 7 days (b) 19 days (c) 28 days (d) 9 days
3. 3.₹507 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹390 (b) ₹39 (c) ₹156 (d) ₹351
4. 4.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 14 days (d) 15 days
5. 5.₹364 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹130 (b) ₹234 (c) ₹182 (d) ₹26
6. 6.₹198 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹162 (b) ₹18 (c) ₹36 (d) ₹99
7. 7.₹184 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹69 (b) ₹92 (c) ₹23 (d) ₹115
8. 8.₹342 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹171 (b) ₹190 (c) ₹152 (d) ₹38
9. 9.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 15 days (c) 11 days (d) 26 days
10. 10.₹480 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹40 (b) ₹240 (c) ₹280 (d) ₹200
11. 11.₹198 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹99 (b) ₹44 (c) ₹22 (d) ₹154
12. 12.7 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 19 days (d) 49 days
13. 13.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 5 days (b) 4 days (c) 6 days (d) 11 days
14. 14.5 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 10 days (b) 4 days (c) 11 days (d) 8 days
15. 15.If 5 kites cost ₹70, how much do 4 kites cost? (a) ₹69 (b) ₹280 (c) ₹70 (d) ₹56
16. 16.If 5 notebooks cost ₹35, how much do 12 notebooks cost? (a) ₹42 (b) ₹420 (c) ₹84 (d) ₹91
17. 17.If 9 pens cost ₹63, how much do 8 pens cost? (a) ₹56 (b) ₹63 (c) ₹62 (d) ₹504
18. 18.If 7 notebooks cost ₹154, how much do 10 notebooks cost? (a) ₹157 (b) ₹220 (c) ₹242 (d) ₹1540
19. 19.If 6 notebooks cost ₹96, how much do 9 notebooks cost? (a) ₹99 (b) ₹144 (c) ₹160 (d) ₹864
20. 20.If 5 pens cost ₹95, how much do 12 pens cost? (a) ₹1140 (b) ₹228 (c) ₹247 (d) ₹102
21. 21.If 6 pens cost ₹36, how much do 3 pens cost? (a) ₹18 (b) ₹108 (c) ₹33 (d) ₹24
22. 22.If 5 notebooks cost ₹70, how much do 2 notebooks cost? (a) ₹42 (b) ₹28 (c) ₹140 (d) ₹67
23. 23.If 6 notebooks cost ₹36, how much do 11 notebooks cost? (a) ₹72 (b) ₹396 (c) ₹41 (d) ₹66
24. 24.If 5 mangoes cost ₹35, how much do 11 mangoes cost? (a) ₹41 (b) ₹84 (c) ₹385 (d) ₹77
25. 25.6 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 42 days (b) 18 days (c) 10 days (d) 43 days
26. 26.₹261 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹58 (b) ₹232 (c) ₹203 (d) ₹29
27. 27.If 4 pens cost ₹64, how much do 10 pens cost? (a) ₹70 (b) ₹176 (c) ₹640 (d) ₹160
28. 28.If 5 kites cost ₹125, how much do 6 kites cost? (a) ₹175 (b) ₹126 (c) ₹150 (d) ₹750
29. 29.3 workers can build a wall in 8 days. How many days will 12 workers take, working at the same speed? (a) 3 days (b) 17 days (c) 2 days (d) 32 days
30. 30.₹161 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹23 (b) ₹139 (c) ₹161 (d) ₹138
31. 31.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 33 days (b) 14 days (c) 32 days (d) 2 days
32. 32.₹533 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹41 (b) ₹410 (c) ₹164 (d) ₹369
33. 33.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 19 days (b) 2 days (c) 18 days (d) 12 days
34. 34.If 9 mangoes cost ₹135, how much do 11 mangoes cost? (a) ₹1485 (b) ₹137 (c) ₹165 (d) ₹180
35. 35.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 3 days (d) 7 days
36. 36.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 15 days (c) 14 days (d) 10 days
37. 37.₹396 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹36 (b) ₹180 (c) ₹216 (d) ₹198
38. 38.₹63 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹56 (b) ₹14 (c) ₹49 (d) ₹7
39. 39.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 1 day (b) 2 days (c) 8 days (d) 3 days
40. 40.₹84 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹7 (b) ₹42 (c) ₹49 (d) ₹35

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