Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 552 · 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 6 mangoes cost ₹126, how much do 2 mangoes cost? (a) ₹122 (b) ₹42 (c) ₹63 (d) ₹252
2. 2.8 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 17 days (d) 10 days
3. 3.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 10 days (c) 6 days (d) 14 days
4. 4.If 9 notebooks cost ₹27, how much do 8 notebooks cost? (a) ₹216 (b) ₹24 (c) ₹27 (d) ₹26
5. 5.₹279 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹186 (b) ₹155 (c) ₹124 (d) ₹31
6. 6.₹374 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹34 (b) ₹170 (c) ₹204 (d) ₹187
7. 7.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 22 days (b) 17 days (c) 21 days (d) 13 days
8. 8.If 5 kites cost ₹25, how much do 11 kites cost? (a) ₹275 (b) ₹60 (c) ₹31 (d) ₹55
9. 9.₹136 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹17 (b) ₹68 (c) ₹119 (d) ₹136
10. 10.If 9 pens cost ₹198, how much do 7 pens cost? (a) ₹176 (b) ₹1386 (c) ₹154 (d) ₹196
11. 11.If 7 pens cost ₹112, how much do 4 pens cost? (a) ₹448 (b) ₹64 (c) ₹109 (d) ₹80
12. 12.If 7 notebooks cost ₹112, how much do 6 notebooks cost? (a) ₹111 (b) ₹672 (c) ₹96 (d) ₹112
13. 13.If 6 notebooks cost ₹48, how much do 2 notebooks cost? (a) ₹44 (b) ₹24 (c) ₹96 (d) ₹16
14. 14.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹78 (b) ₹13 (c) ₹65 (d) ₹52
15. 15.9 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 5 days (b) 1 day (c) 7 days (d) 6 days
16. 16.6 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 24 days (b) 4 days (c) 25 days (d) 12 days
17. 17.₹528 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹288 (b) ₹48 (c) ₹240 (d) ₹264
18. 18.If 5 kites cost ₹35, how much do 11 kites cost? (a) ₹84 (b) ₹77 (c) ₹385 (d) ₹41
19. 19.If 2 pens cost ₹6, how much do 3 pens cost? (a) ₹7 (b) ₹12 (c) ₹9 (d) ₹18
20. 20.₹90 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹90 (b) ₹9 (c) ₹45 (d) ₹81
21. 21.If 9 notebooks cost ₹63, how much do 12 notebooks cost? (a) ₹756 (b) ₹91 (c) ₹84 (d) ₹66
22. 22.6 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 4 days (b) 7 days (c) 5 days (d) 6 days
23. 23.If 4 kites cost ₹64, how much do 6 kites cost? (a) ₹384 (b) ₹66 (c) ₹96 (d) ₹112
24. 24.If 3 mangoes cost ₹12, how much do 10 mangoes cost? (a) ₹120 (b) ₹19 (c) ₹44 (d) ₹40
25. 25.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 3 days (c) 4 days (d) 8 days
26. 26.4 workers can build a wall in 15 days. How many days will 12 workers take, working at the same speed? (a) 45 days (b) 5 days (c) 7 days (d) 23 days
27. 27.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 2 days (b) 11 days (c) 1 day (d) 3 days
28. 28.If 6 pens cost ₹102, how much do 7 pens cost? (a) ₹714 (b) ₹103 (c) ₹119 (d) ₹136
29. 29.₹72 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹36 (b) ₹9 (c) ₹72 (d) ₹63
30. 30.6 workers can build a wall in 11 days. How many days will 3 workers take, working at the same speed? (a) 8 days (b) 14 days (c) 22 days (d) 23 days
31. 31.If 8 kites cost ₹72, how much do 5 kites cost? (a) ₹69 (b) ₹45 (c) ₹360 (d) ₹54
32. 32.If 5 notebooks cost ₹70, how much do 6 notebooks cost? (a) ₹420 (b) ₹84 (c) ₹98 (d) ₹71
33. 33.If 5 pens cost ₹30, how much do 2 pens cost? (a) ₹27 (b) ₹18 (c) ₹60 (d) ₹12
34. 34.8 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 7 days (c) 17 days (d) 16 days
35. 35.If 8 pens cost ₹152, how much do 9 pens cost? (a) ₹153 (b) ₹190 (c) ₹1368 (d) ₹171
36. 36.If 9 notebooks cost ₹36, how much do 8 notebooks cost? (a) ₹36 (b) ₹35 (c) ₹288 (d) ₹32
37. 37.If 2 mangoes cost ₹14, how much do 12 mangoes cost? (a) ₹84 (b) ₹24 (c) ₹168 (d) ₹91
38. 38.5 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 11 days (d) 7 days
39. 39.₹230 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹115 (b) ₹69 (c) ₹161 (d) ₹23
40. 40.If 7 kites cost ₹98, how much do 8 kites cost? (a) ₹99 (b) ₹112 (c) ₹126 (d) ₹784

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