Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 245 · 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. 1.9 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 8 days (b) 13 days (c) 9 days (d) 10 days
2. 2.If 7 notebooks cost ₹77, how much do 5 notebooks cost? (a) ₹55 (b) ₹385 (c) ₹75 (d) ₹66
3. 3.₹216 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹168 (b) ₹48 (c) ₹108 (d) ₹24
4. 4.If 3 mangoes cost ₹33, how much do 8 mangoes cost? (a) ₹38 (b) ₹264 (c) ₹99 (d) ₹88
5. 5.If 8 pens cost ₹24, how much do 7 pens cost? (a) ₹21 (b) ₹24 (c) ₹23 (d) ₹168
6. 6.If 9 mangoes cost ₹36, how much do 3 mangoes cost? (a) ₹30 (b) ₹108 (c) ₹16 (d) ₹12
7. 7.If 8 kites cost ₹40, how much do 7 kites cost? (a) ₹280 (b) ₹39 (c) ₹35 (d) ₹40
8. 8.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 19 days (b) 28 days (c) 11 days (d) 27 days
9. 9.₹336 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹336 (b) ₹48 (c) ₹168 (d) ₹288
10. 10.If 9 notebooks cost ₹36, how much do 11 notebooks cost? (a) ₹48 (b) ₹38 (c) ₹44 (d) ₹396
11. 11.₹156 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹65 (b) ₹78 (c) ₹91 (d) ₹13
12. 12.₹153 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹137 (b) ₹17 (c) ₹136 (d) ₹153
13. 13.₹351 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹27 (b) ₹135 (c) ₹243 (d) ₹216
14. 14.9 workers can build a wall in 14 days. How many days will 6 workers take, working at the same speed? (a) 21 days (b) 11 days (c) 17 days (d) 22 days
15. 15.₹576 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹288 (b) ₹240 (c) ₹336 (d) ₹48
16. 16.4 workers can build a wall in 12 days. How many days will 12 workers take, working at the same speed? (a) 20 days (b) 5 days (c) 36 days (d) 4 days
17. 17.If 9 notebooks cost ₹189, how much do 8 notebooks cost? (a) ₹1512 (b) ₹188 (c) ₹168 (d) ₹189
18. 18.If 4 pens cost ₹92, how much do 5 pens cost? (a) ₹115 (b) ₹93 (c) ₹138 (d) ₹460
19. 19.₹312 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹26 (b) ₹182 (c) ₹130 (d) ₹156
20. 20.3 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) 2 days (d) 3 days
21. 21.₹450 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹250 (b) ₹225 (c) ₹50 (d) ₹200
22. 22.4 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 6 days (c) 9 days (d) 8 days
23. 23.₹99 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹55 (b) ₹66 (c) ₹44 (d) ₹11
24. 24.₹280 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹140 (b) ₹252 (c) ₹28 (d) ₹280
25. 25.If 7 kites cost ₹133, how much do 12 kites cost? (a) ₹228 (b) ₹138 (c) ₹247 (d) ₹1596
26. 26.₹182 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹130 (b) ₹26 (c) ₹52 (d) ₹91
27. 27.If 6 mangoes cost ₹72, how much do 4 mangoes cost? (a) ₹48 (b) ₹288 (c) ₹60 (d) ₹70
28. 28.₹600 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹50 (b) ₹300 (c) ₹350 (d) ₹250
29. 29.3 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) 3 days (d) 11 days
30. 30.7 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 1 day (b) 22 days (c) 21 days (d) 11 days
31. 31.If 2 pens cost ₹26, how much do 4 pens cost? (a) ₹104 (b) ₹65 (c) ₹52 (d) ₹28
32. 32.₹80 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹80 (b) ₹20 (c) ₹40 (d) ₹60
33. 33.₹342 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹266 (b) ₹171 (c) ₹38 (d) ₹76
34. 34.₹117 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹78 (b) ₹65 (c) ₹13 (d) ₹52
35. 35.₹312 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹24 (b) ₹156 (c) ₹96 (d) ₹216
36. 36.5 workers can build a wall in 12 days. How many days will 6 workers take, working at the same speed? (a) 11 days (b) 10 days (c) 13 days (d) 9 days
37. 37.₹80 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹80 (b) ₹8 (c) ₹72 (d) ₹40
38. 38.8 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 2 days (b) 32 days (c) 14 days (d) 33 days
39. 39.If 8 pens cost ₹48, how much do 11 pens cost? (a) ₹528 (b) ₹72 (c) ₹51 (d) ₹66
40. 40.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 2 days (c) 10 days (d) 14 days

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