Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 254 · 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.₹517 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹376 (b) ₹329 (c) ₹188 (d) ₹47
2. 2.If 3 pens cost ₹39, how much do 5 pens cost? (a) ₹65 (b) ₹41 (c) ₹78 (d) ₹195
3. 3.₹189 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹147 (b) ₹168 (c) ₹42 (d) ₹21
4. 4.3 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 3 days (b) 4 days (c) 2 days (d) 17 days
5. 5.₹56 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹28 (b) ₹49 (c) ₹56 (d) ₹7
6. 6.5 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 16 days (c) 12 days (d) 11 days
7. 7.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 20 days (d) 15 days
8. 8.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 17 days (b) 9 days (c) 40 days (d) 39 days
9. 9.If 4 notebooks cost ₹24, how much do 2 notebooks cost? (a) ₹18 (b) ₹12 (c) ₹22 (d) ₹48
10. 10.₹98 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹49 (b) ₹28 (c) ₹70 (d) ₹14
11. 11.₹208 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹104 (b) ₹64 (c) ₹144 (d) ₹16
12. 12.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 5 days (d) 17 days
13. 13.₹242 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹121 (b) ₹22 (c) ₹176 (d) ₹66
14. 14.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 3 days (b) 22 days (c) 11 days (d) 21 days
15. 15.₹231 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹33 (b) ₹199 (c) ₹231 (d) ₹198
16. 16.If 9 kites cost ₹90, how much do 4 kites cost? (a) ₹85 (b) ₹50 (c) ₹40 (d) ₹360
17. 17.If 4 pens cost ₹64, how much do 12 pens cost? (a) ₹72 (b) ₹192 (c) ₹208 (d) ₹768
18. 18.If 3 notebooks cost ₹15, how much do 9 notebooks cost? (a) ₹45 (b) ₹50 (c) ₹135 (d) ₹21
19. 19.If 8 mangoes cost ₹88, how much do 6 mangoes cost? (a) ₹66 (b) ₹77 (c) ₹528 (d) ₹86
20. 20.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 32 days (b) 14 days (c) 33 days (d) 2 days
21. 21.₹85 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹69 (d) ₹85
22. 22.₹480 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹48 (b) ₹240 (c) ₹336 (d) ₹144
23. 23.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹96 (b) ₹16 (c) ₹80 (d) ₹112
24. 24.If 3 notebooks cost ₹69, how much do 4 notebooks cost? (a) ₹70 (b) ₹115 (c) ₹92 (d) ₹276
25. 25.₹36 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹24 (b) ₹36 (c) ₹18 (d) ₹12
26. 26.If 8 notebooks cost ₹112, how much do 3 notebooks cost? (a) ₹336 (b) ₹42 (c) ₹107 (d) ₹56
27. 27.If 2 pens cost ₹22, how much do 10 pens cost? (a) ₹30 (b) ₹110 (c) ₹121 (d) ₹220
28. 28.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 9 days (c) 6 days (d) 8 days
29. 29.9 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 8 days (b) 10 days (c) 9 days (d) 5 days
30. 30.If 7 pens cost ₹84, how much do 11 pens cost? (a) ₹144 (b) ₹132 (c) ₹924 (d) ₹88
31. 31.₹228 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹133 (b) ₹114 (c) ₹95 (d) ₹19
32. 32.₹637 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹49 (b) ₹245 (c) ₹392 (d) ₹441
33. 33.3 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 28 days (b) 17 days (c) 7 days (d) 11 days
34. 34.If 2 pens cost ₹30, how much do 8 pens cost? (a) ₹135 (b) ₹240 (c) ₹36 (d) ₹120
35. 35.₹220 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹140 (b) ₹80 (c) ₹20 (d) ₹110
36. 36.₹231 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹21 (b) ₹168 (c) ₹84 (d) ₹147
37. 37.If 9 kites cost ₹216, how much do 12 kites cost? (a) ₹312 (b) ₹2592 (c) ₹219 (d) ₹288
38. 38.8 workers can build a wall in 6 days. How many days will 12 workers take, working at the same speed? (a) 4 days (b) 9 days (c) 2 days (d) 10 days
39. 39.4 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 5 days (c) 20 days (d) 12 days
40. 40.If 3 pens cost ₹9, how much do 2 pens cost? (a) ₹9 (b) ₹8 (c) ₹6 (d) ₹18

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