Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 110 · 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. 1.6 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 9 days (c) 3 days (d) 4 days
2. 2.If 6 pens cost ₹138, how much do 5 pens cost? (a) ₹138 (b) ₹137 (c) ₹690 (d) ₹115
3. 3.₹372 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹155 (b) ₹217 (c) ₹186 (d) ₹31
4. 4.If 2 mangoes cost ₹26, how much do 4 mangoes cost? (a) ₹28 (b) ₹65 (c) ₹104 (d) ₹52
5. 5.If 2 notebooks cost ₹40, how much do 5 notebooks cost? (a) ₹43 (b) ₹200 (c) ₹100 (d) ₹120
6. 6.6 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 12 days (b) 11 days (c) 13 days (d) 15 days
7. 7.4 workers can build a wall in 10 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 20 days (d) 14 days
8. 8.If 8 mangoes cost ₹200, how much do 7 mangoes cost? (a) ₹200 (b) ₹175 (c) ₹1400 (d) ₹199
9. 9.₹297 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹165 (b) ₹132 (c) ₹33 (d) ₹198
10. 10.If 4 mangoes cost ₹12, how much do 2 mangoes cost? (a) ₹24 (b) ₹10 (c) ₹6 (d) ₹9
11. 11.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 4 days (b) 19 days (c) 2 days (d) 3 days
12. 12.4 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 8 days (b) 4 days (c) 3 days (d) 12 days
13. 13.If 9 pens cost ₹45, how much do 11 pens cost? (a) ₹47 (b) ₹55 (c) ₹495 (d) ₹60
14. 14.3 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 4 days (b) 3 days (c) 11 days (d) 2 days
15. 15.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 21 days (d) 22 days
16. 16.3 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 7 days (d) 4 days
17. 17.₹56 is shared between two friends in the ratio 3 : 4. How much is the bigger share? (a) ₹24 (b) ₹8 (c) ₹32 (d) ₹28
18. 18.If 3 kites cost ₹75, how much do 12 kites cost? (a) ₹325 (b) ₹300 (c) ₹84 (d) ₹900
19. 19.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 44 days (b) 45 days (c) 17 days (d) 5 days
20. 20.If 2 mangoes cost ₹24, how much do 11 mangoes cost? (a) ₹144 (b) ₹33 (c) ₹264 (d) ₹132
21. 21.If 9 notebooks cost ₹171, how much do 10 notebooks cost? (a) ₹1710 (b) ₹190 (c) ₹209 (d) ₹172
22. 22.If 3 pens cost ₹72, how much do 10 pens cost? (a) ₹720 (b) ₹264 (c) ₹79 (d) ₹240
23. 23.₹80 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹32 (b) ₹16 (c) ₹40 (d) ₹48
24. 24.3 workers can build a wall in 8 days. How many days will 4 workers take, working at the same speed? (a) 6 days (b) 9 days (c) 7 days (d) 5 days
25. 25.6 workers can build a wall in 5 days. How many days will 3 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 2 days (d) 8 days
26. 26.If 4 kites cost ₹28, how much do 3 kites cost? (a) ₹27 (b) ₹28 (c) ₹84 (d) ₹21
27. 27.If 6 notebooks cost ₹30, how much do 5 notebooks cost? (a) ₹150 (b) ₹25 (c) ₹30 (d) ₹29
28. 28.If 9 mangoes cost ₹216, how much do 10 mangoes cost? (a) ₹2160 (b) ₹217 (c) ₹240 (d) ₹264
29. 29.₹180 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹54 (b) ₹18 (c) ₹126 (d) ₹90
30. 30.₹176 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹88 (b) ₹22 (c) ₹154 (d) ₹176
31. 31.9 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 14 days (c) 18 days (d) 6 days
32. 32.7 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 35 days (b) 19 days (c) 11 days (d) 36 days
33. 33.If 9 mangoes cost ₹72, how much do 11 mangoes cost? (a) ₹88 (b) ₹96 (c) ₹74 (d) ₹792
34. 34.₹160 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹96 (b) ₹80 (c) ₹32 (d) ₹64
35. 35.6 workers can build a wall in 6 days. How many days will 9 workers take, working at the same speed? (a) 5 days (b) 3 days (c) 4 days (d) 9 days
36. 36.8 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 28 days (c) 29 days (d) 1 day
37. 37.If 8 mangoes cost ₹48, how much do 10 mangoes cost? (a) ₹50 (b) ₹66 (c) ₹480 (d) ₹60
38. 38.If 7 mangoes cost ₹28, how much do 4 mangoes cost? (a) ₹25 (b) ₹16 (c) ₹112 (d) ₹20
39. 39.If 6 kites cost ₹24, how much do 4 kites cost? (a) ₹96 (b) ₹22 (c) ₹20 (d) ₹16
40. 40.₹42 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹30 (b) ₹12 (c) ₹6 (d) ₹21

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