Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 581 · 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. 1.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 5 days (c) 9 days (d) 6 days
2. 2.If 8 pens cost ₹192, how much do 6 pens cost? (a) ₹190 (b) ₹168 (c) ₹144 (d) ₹1152
3. 3.If 3 mangoes cost ₹66, how much do 8 mangoes cost? (a) ₹176 (b) ₹198 (c) ₹71 (d) ₹528
4. 4.9 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 18 days (b) 15 days (c) 8 days (d) 9 days
5. 5.₹77 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹28 (b) ₹7 (c) ₹56 (d) ₹49
6. 6.If 8 pens cost ₹72, how much do 2 pens cost? (a) ₹144 (b) ₹66 (c) ₹27 (d) ₹18
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) 15 days (c) 5 days (d) 20 days
8. 8.₹387 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹387 (b) ₹43 (c) ₹345 (d) ₹344
9. 9.₹80 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹48 (b) ₹40 (c) ₹16 (d) ₹32
10. 10.₹220 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹40 (b) ₹110 (c) ₹180 (d) ₹20
11. 11.If 5 pens cost ₹25, how much do 6 pens cost? (a) ₹26 (b) ₹30 (c) ₹150 (d) ₹35
12. 12.₹280 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹140 (b) ₹240 (c) ₹280 (d) ₹40
13. 13.₹165 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹15 (b) ₹120 (c) ₹60 (d) ₹105
14. 14.If 7 notebooks cost ₹112, how much do 4 notebooks cost? (a) ₹64 (b) ₹109 (c) ₹80 (d) ₹448
15. 15.₹270 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹120 (b) ₹30 (c) ₹135 (d) ₹150
16. 16.₹175 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹75 (b) ₹100 (c) ₹125 (d) ₹25
17. 17.If 3 notebooks cost ₹27, how much do 6 notebooks cost? (a) ₹162 (b) ₹63 (c) ₹54 (d) ₹30
18. 18.₹264 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹132 (b) ₹48 (c) ₹24 (d) ₹216
19. 19.₹110 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹55 (b) ₹88 (c) ₹110 (d) ₹22
20. 20.If 6 pens cost ₹42, how much do 10 pens cost? (a) ₹420 (b) ₹77 (c) ₹46 (d) ₹70
21. 21.If 2 notebooks cost ₹8, how much do 4 notebooks cost? (a) ₹10 (b) ₹20 (c) ₹32 (d) ₹16
22. 22.If 2 mangoes cost ₹42, how much do 7 mangoes cost? (a) ₹47 (b) ₹294 (c) ₹168 (d) ₹147
23. 23.₹55 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹5 (b) ₹10 (c) ₹50 (d) ₹45
24. 24.₹129 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹43 (b) ₹86 (c) ₹87 (d) ₹129
25. 25.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹91 (b) ₹112 (c) ₹14 (d) ₹70
26. 26.₹117 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹26 (b) ₹13 (c) ₹91 (d) ₹104
27. 27.7 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 36 days (c) 35 days (d) 5 days
28. 28.₹441 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹49 (b) ₹392 (c) ₹98 (d) ₹343
29. 29.If 2 notebooks cost ₹22, how much do 11 notebooks cost? (a) ₹121 (b) ₹242 (c) ₹31 (d) ₹132
30. 30.4 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 14 days (c) 5 days (d) 15 days
31. 31.If 8 notebooks cost ₹88, how much do 9 notebooks cost? (a) ₹110 (b) ₹89 (c) ₹99 (d) ₹792
32. 32.₹192 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹96 (b) ₹80 (c) ₹112 (d) ₹16
33. 33.If 5 pens cost ₹120, how much do 4 pens cost? (a) ₹119 (b) ₹96 (c) ₹120 (d) ₹480
34. 34.If 4 kites cost ₹28, how much do 3 kites cost? (a) ₹84 (b) ₹21 (c) ₹27 (d) ₹28
35. 35.If 3 kites cost ₹39, how much do 5 kites cost? (a) ₹195 (b) ₹78 (c) ₹65 (d) ₹41
36. 36.₹396 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹36 (b) ₹144 (c) ₹198 (d) ₹252
37. 37.₹333 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹185 (b) ₹222 (c) ₹37 (d) ₹148
38. 38.4 workers can build a wall in 15 days. How many days will 6 workers take, working at the same speed? (a) 13 days (b) 10 days (c) 11 days (d) 17 days
39. 39.If 3 kites cost ₹63, how much do 6 kites cost? (a) ₹378 (b) ₹126 (c) ₹147 (d) ₹66
40. 40.₹192 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹192 (b) ₹32 (c) ₹96 (d) ₹160

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