Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 875 · 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 3 mangoes cost ₹42, how much do 4 mangoes cost? (a) ₹70 (b) ₹168 (c) ₹43 (d) ₹56
2. 2.₹308 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹252 (b) ₹154 (c) ₹28 (d) ₹56
3. 3.₹147 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹147 (b) ₹126 (c) ₹127 (d) ₹21
4. 4.₹98 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹7 (b) ₹49 (c) ₹63 (d) ₹35
5. 5.If 8 mangoes cost ₹72, how much do 5 mangoes cost? (a) ₹69 (b) ₹360 (c) ₹54 (d) ₹45
6. 6.4 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 25 days (b) 4 days (c) 16 days (d) 5 days
7. 7.4 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 7 days (d) 8 days
8. 8.₹351 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹312 (b) ₹39 (c) ₹273 (d) ₹78
9. 9.If 6 mangoes cost ₹96, how much do 11 mangoes cost? (a) ₹176 (b) ₹192 (c) ₹1056 (d) ₹101
10. 10.If 3 notebooks cost ₹18, how much do 6 notebooks cost? (a) ₹108 (b) ₹42 (c) ₹21 (d) ₹36
11. 11.8 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 10 days (b) 19 days (c) 9 days (d) 11 days
12. 12.If 4 kites cost ₹16, how much do 9 kites cost? (a) ₹40 (b) ₹21 (c) ₹36 (d) ₹144
13. 13.If 9 pens cost ₹180, how much do 7 pens cost? (a) ₹160 (b) ₹178 (c) ₹140 (d) ₹1260
14. 14.If 6 mangoes cost ₹132, how much do 7 mangoes cost? (a) ₹154 (b) ₹133 (c) ₹176 (d) ₹924
15. 15.If 4 kites cost ₹36, how much do 11 kites cost? (a) ₹396 (b) ₹99 (c) ₹108 (d) ₹43
16. 16.If 2 kites cost ₹6, how much do 7 kites cost? (a) ₹11 (b) ₹42 (c) ₹21 (d) ₹24
17. 17.If 4 notebooks cost ₹96, how much do 5 notebooks cost? (a) ₹144 (b) ₹97 (c) ₹480 (d) ₹120
18. 18.₹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
19. 19.₹495 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹45 (b) ₹135 (c) ₹405 (d) ₹360
20. 20.If 9 pens cost ₹126, how much do 8 pens cost? (a) ₹1008 (b) ₹112 (c) ₹125 (d) ₹126
21. 21.If 6 mangoes cost ₹120, how much do 3 mangoes cost? (a) ₹60 (b) ₹117 (c) ₹360 (d) ₹80
22. 22.3 workers can build a wall in 4 days. How many days will 4 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 5 days
23. 23.If 8 kites cost ₹104, how much do 7 kites cost? (a) ₹728 (b) ₹104 (c) ₹103 (d) ₹91
24. 24.If 4 pens cost ₹28, how much do 12 pens cost? (a) ₹36 (b) ₹84 (c) ₹336 (d) ₹91
25. 25.If 6 notebooks cost ₹30, how much do 11 notebooks cost? (a) ₹330 (b) ₹60 (c) ₹55 (d) ₹35
26. 26.₹72 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹12 (b) ₹60 (c) ₹72 (d) ₹36
27. 27.If 4 kites cost ₹48, how much do 5 kites cost? (a) ₹60 (b) ₹72 (c) ₹49 (d) ₹240
28. 28.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 28 days (b) 3 days (c) 27 days (d) 15 days
29. 29.If 3 mangoes cost ₹45, how much do 10 mangoes cost? (a) ₹450 (b) ₹52 (c) ₹150 (d) ₹165
30. 30.If 2 pens cost ₹24, how much do 5 pens cost? (a) ₹72 (b) ₹60 (c) ₹27 (d) ₹120
31. 31.7 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 7 days (b) 8 days (c) 6 days (d) 15 days
32. 32.If 5 pens cost ₹30, how much do 4 pens cost? (a) ₹29 (b) ₹24 (c) ₹30 (d) ₹120
33. 33.If 6 kites cost ₹30, how much do 7 kites cost? (a) ₹31 (b) ₹40 (c) ₹210 (d) ₹35
34. 34.If 4 pens cost ₹40, how much do 3 pens cost? (a) ₹120 (b) ₹39 (c) ₹40 (d) ₹30
35. 35.9 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 19 days (c) 11 days (d) 18 days
36. 36.7 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 15 days (c) 9 days (d) 14 days
37. 37.If 7 notebooks cost ₹119, how much do 8 notebooks cost? (a) ₹120 (b) ₹136 (c) ₹153 (d) ₹952
38. 38.₹55 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹5 (b) ₹40 (c) ₹35 (d) ₹20
39. 39.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 7 days (b) 6 days (c) 11 days (d) 8 days
40. 40.3 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 13 days

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