Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 421 · 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 8 pens cost ₹136, how much do 4 pens cost? (a) ₹85 (b) ₹544 (c) ₹132 (d) ₹68
2. 2.9 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 27 days (c) 3 days (d) 28 days
3. 3.If 4 pens cost ₹68, how much do 9 pens cost? (a) ₹153 (b) ₹170 (c) ₹612 (d) ₹73
4. 4.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹350 (b) ₹50 (c) ₹250 (d) ₹300
5. 5.8 workers can build a wall in 13 days. How many days will 4 workers take, working at the same speed? (a) 17 days (b) 26 days (c) 9 days (d) 27 days
6. 6.If 2 mangoes cost ₹10, how much do 12 mangoes cost? (a) ₹60 (b) ₹120 (c) ₹65 (d) ₹20
7. 7.7 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 11 days (c) 14 days (d) 15 days
8. 8.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 28 days (b) 13 days (c) 1 day (d) 29 days
9. 9.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 6 days (c) 5 days (d) 9 days
10. 10.If 2 pens cost ₹16, how much do 4 pens cost? (a) ₹18 (b) ₹40 (c) ₹64 (d) ₹32
11. 11.₹162 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹81 (b) ₹27 (c) ₹135 (d) ₹162
12. 12.₹209 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹19 (b) ₹38 (c) ₹171 (d) ₹190
13. 13.If 4 mangoes cost ₹48, how much do 5 mangoes cost? (a) ₹49 (b) ₹60 (c) ₹72 (d) ₹240
14. 14.If 6 pens cost ₹78, how much do 9 pens cost? (a) ₹81 (b) ₹130 (c) ₹117 (d) ₹702
15. 15.If 7 mangoes cost ₹161, how much do 5 mangoes cost? (a) ₹805 (b) ₹159 (c) ₹138 (d) ₹115
16. 16.If 3 notebooks cost ₹54, how much do 12 notebooks cost? (a) ₹648 (b) ₹234 (c) ₹63 (d) ₹216
17. 17.₹68 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹34 (b) ₹17 (c) ₹51 (d) ₹68
18. 18.If 6 kites cost ₹108, how much do 5 kites cost? (a) ₹107 (b) ₹540 (c) ₹108 (d) ₹90
19. 19.₹50 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹5 (b) ₹25 (c) ₹50 (d) ₹45
20. 20.If 8 kites cost ₹88, how much do 10 kites cost? (a) ₹121 (b) ₹880 (c) ₹90 (d) ₹110
21. 21.₹81 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹36 (b) ₹45 (c) ₹54 (d) ₹9
22. 22.If 2 pens cost ₹36, how much do 5 pens cost? (a) ₹108 (b) ₹39 (c) ₹90 (d) ₹180
23. 23.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 10 days (b) 13 days (c) 9 days (d) 8 days
24. 24.8 workers can build a wall in 5 days. How many days will 4 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 9 days (d) 10 days
25. 25.₹300 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹210 (b) ₹150 (c) ₹90 (d) ₹30
26. 26.₹484 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹242 (b) ₹44 (c) ₹220 (d) ₹264
27. 27.₹175 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹35 (b) ₹140 (c) ₹105 (d) ₹70
28. 28.If 4 notebooks cost ₹52, how much do 2 notebooks cost? (a) ₹50 (b) ₹26 (c) ₹104 (d) ₹39
29. 29.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹22 (b) ₹110 (c) ₹88 (d) ₹99
30. 30.If 4 mangoes cost ₹68, how much do 11 mangoes cost? (a) ₹748 (b) ₹204 (c) ₹187 (d) ₹75
31. 31.₹440 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹240 (b) ₹220 (c) ₹200 (d) ₹40
32. 32.If 7 pens cost ₹56, how much do 8 pens cost? (a) ₹72 (b) ₹64 (c) ₹448 (d) ₹57
33. 33.4 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 8 days (b) 7 days (c) 11 days (d) 9 days
34. 34.₹407 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹296 (b) ₹37 (c) ₹259 (d) ₹148
35. 35.₹301 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹301 (b) ₹259 (c) ₹258 (d) ₹43
36. 36.If 5 mangoes cost ₹115, how much do 2 mangoes cost? (a) ₹69 (b) ₹46 (c) ₹230 (d) ₹112
37. 37.4 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 23 days (b) 13 days (c) 9 days (d) 22 days
38. 38.If 4 kites cost ₹60, how much do 12 kites cost? (a) ₹195 (b) ₹180 (c) ₹720 (d) ₹68
39. 39.If 4 pens cost ₹84, how much do 10 pens cost? (a) ₹231 (b) ₹90 (c) ₹210 (d) ₹840
40. 40.If 4 pens cost ₹56, how much do 8 pens cost? (a) ₹448 (b) ₹60 (c) ₹126 (d) ₹112

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