Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 973 · 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 mangoes cost ₹40, how much do 6 mangoes cost? (a) ₹120 (b) ₹44 (c) ₹240 (d) ₹140
2. 2.If 5 notebooks cost ₹85, how much do 6 notebooks cost? (a) ₹102 (b) ₹86 (c) ₹119 (d) ₹510
3. 3.If 9 mangoes cost ₹135, how much do 10 mangoes cost? (a) ₹150 (b) ₹165 (c) ₹136 (d) ₹1350
4. 4.If 4 pens cost ₹48, how much do 3 pens cost? (a) ₹48 (b) ₹36 (c) ₹144 (d) ₹47
5. 5.If 7 pens cost ₹175, how much do 8 pens cost? (a) ₹1400 (b) ₹200 (c) ₹176 (d) ₹225
6. 6.₹243 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹135 (b) ₹162 (c) ₹27 (d) ₹108
7. 7.If 3 pens cost ₹9, how much do 4 pens cost? (a) ₹10 (b) ₹12 (c) ₹36 (d) ₹15
8. 8.If 5 notebooks cost ₹110, how much do 10 notebooks cost? (a) ₹220 (b) ₹115 (c) ₹242 (d) ₹1100
9. 9.5 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 16 days (c) 7 days (d) 15 days
10. 10.₹133 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹38 (b) ₹19 (c) ₹114 (d) ₹95
11. 11.₹90 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹90 (b) ₹45 (c) ₹72 (d) ₹18
12. 12.If 9 notebooks cost ₹117, how much do 10 notebooks cost? (a) ₹130 (b) ₹1170 (c) ₹143 (d) ₹118
13. 13.If 3 mangoes cost ₹75, how much do 6 mangoes cost? (a) ₹175 (b) ₹450 (c) ₹78 (d) ₹150
14. 14.₹360 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹180 (b) ₹360 (c) ₹40 (d) ₹320
15. 15.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 27 days (b) 26 days (c) 28 days (d) 13 days
16. 16.₹156 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹78 (b) ₹96 (c) ₹12 (d) ₹60
17. 17.₹432 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹48 (b) ₹216 (c) ₹192 (d) ₹240
18. 18.If 5 pens cost ₹45, how much do 8 pens cost? (a) ₹72 (b) ₹48 (c) ₹360 (d) ₹81
19. 19.9 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 12 days (b) 2 days (c) 19 days (d) 18 days
20. 20.₹150 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹150 (b) ₹100 (c) ₹75 (d) ₹50
21. 21.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 7 days
22. 22.₹230 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹46 (b) ₹115 (c) ₹138 (d) ₹92
23. 23.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 23 days (d) 22 days
24. 24.₹187 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹102 (b) ₹119 (c) ₹85 (d) ₹17
25. 25.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 2 days (b) 4 days (c) 11 days (d) 3 days
26. 26.9 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 2 days (b) 24 days (c) 25 days (d) 14 days
27. 27.If 8 mangoes cost ₹112, how much do 7 mangoes cost? (a) ₹98 (b) ₹111 (c) ₹784 (d) ₹112
28. 28.If 6 notebooks cost ₹108, how much do 9 notebooks cost? (a) ₹111 (b) ₹972 (c) ₹180 (d) ₹162
29. 29.If 3 mangoes cost ₹63, how much do 12 mangoes cost? (a) ₹756 (b) ₹72 (c) ₹273 (d) ₹252
30. 30.If 3 notebooks cost ₹12, how much do 4 notebooks cost? (a) ₹20 (b) ₹48 (c) ₹13 (d) ₹16
31. 31.₹78 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹39 (b) ₹26 (c) ₹78 (d) ₹52
32. 32.₹369 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹329 (b) ₹369 (c) ₹41 (d) ₹328
33. 33.₹325 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹100 (b) ₹25 (c) ₹225 (d) ₹250
34. 34.₹280 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹140 (b) ₹200 (c) ₹40 (d) ₹80
35. 35.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 9 days (d) 13 days
36. 36.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 5 days (c) 6 days (d) 4 days
37. 37.If 8 kites cost ₹184, how much do 2 kites cost? (a) ₹178 (b) ₹69 (c) ₹46 (d) ₹368
38. 38.₹225 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹25 (b) ₹125 (c) ₹100 (d) ₹150
39. 39.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 4 days (c) 10 days (d) 14 days
40. 40.If 3 notebooks cost ₹66, how much do 4 notebooks cost? (a) ₹88 (b) ₹67 (c) ₹110 (d) ₹264

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