Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 673 · 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.₹232 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹116 (b) ₹87 (c) ₹145 (d) ₹29
2. 2.If 4 kites cost ₹64, how much do 2 kites cost? (a) ₹62 (b) ₹128 (c) ₹48 (d) ₹32
3. 3.₹329 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹282 (b) ₹47 (c) ₹329 (d) ₹283
4. 4.If 4 notebooks cost ₹80, how much do 6 notebooks cost? (a) ₹140 (b) ₹480 (c) ₹82 (d) ₹120
5. 5.If 7 notebooks cost ₹77, how much do 2 notebooks cost? (a) ₹22 (b) ₹154 (c) ₹33 (d) ₹72
6. 6.8 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 45 days (c) 17 days (d) 44 days
7. 7.7 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 13 days (d) 22 days
8. 8.₹160 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹140 (b) ₹80 (c) ₹20 (d) ₹160
9. 9.9 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 27 days (b) 28 days (c) 19 days (d) 11 days
10. 10.If 9 pens cost ₹198, how much do 10 pens cost? (a) ₹220 (b) ₹242 (c) ₹1980 (d) ₹199
11. 11.If 4 notebooks cost ₹52, how much do 6 notebooks cost? (a) ₹312 (b) ₹91 (c) ₹54 (d) ₹78
12. 12.If 9 kites cost ₹117, how much do 11 kites cost? (a) ₹119 (b) ₹156 (c) ₹1287 (d) ₹143
13. 13.8 workers can build a wall in 9 days. How many days will 12 workers take, working at the same speed? (a) 7 days (b) 13 days (c) 6 days (d) 5 days
14. 14.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹70 (b) ₹14 (c) ₹112 (d) ₹91
15. 15.4 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 14 days (b) 6 days (c) 10 days (d) 24 days
16. 16.6 workers can build a wall in 13 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 26 days (c) 27 days (d) 10 days
17. 17.₹352 is shared between two friends in the ratio 3 : 8. How much is the bigger share? (a) ₹176 (b) ₹96 (c) ₹256 (d) ₹32
18. 18.If 4 notebooks cost ₹64, how much do 7 notebooks cost? (a) ₹448 (b) ₹128 (c) ₹112 (d) ₹67
19. 19.If 3 mangoes cost ₹42, how much do 4 mangoes cost? (a) ₹168 (b) ₹56 (c) ₹70 (d) ₹43
20. 20.5 workers can build a wall in 6 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 5 days (c) 6 days (d) 4 days
21. 21.₹230 is shared between two friends in the ratio 1 : 4. How much is the bigger share? (a) ₹230 (b) ₹184 (c) ₹46 (d) ₹115
22. 22.9 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 10 days (b) 9 days (c) 7 days (d) 8 days
23. 23.7 workers can build a wall in 15 days. How many days will 5 workers take, working at the same speed? (a) 13 days (b) 17 days (c) 22 days (d) 21 days
24. 24.₹120 is shared between two friends in the ratio 1 : 5. How much is the bigger share? (a) ₹20 (b) ₹60 (c) ₹120 (d) ₹100
25. 25.3 workers can build a wall in 4 days. How many days will 6 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 8 days (d) 1 day
26. 26.If 6 pens cost ₹30, how much do 8 pens cost? (a) ₹40 (b) ₹45 (c) ₹240 (d) ₹32
27. 27.6 workers can build a wall in 14 days. How many days will 3 workers take, working at the same speed? (a) 17 days (b) 28 days (c) 7 days (d) 11 days
28. 28.₹99 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹9 (b) ₹72 (c) ₹36 (d) ₹63
29. 29.If 3 notebooks cost ₹54, how much do 4 notebooks cost? (a) ₹55 (b) ₹90 (c) ₹72 (d) ₹216
30. 30.If 9 kites cost ₹54, how much do 5 kites cost? (a) ₹36 (b) ₹50 (c) ₹30 (d) ₹270
31. 31.If 7 kites cost ₹105, how much do 9 kites cost? (a) ₹945 (b) ₹135 (c) ₹107 (d) ₹150
32. 32.If 9 pens cost ₹180, how much do 11 pens cost? (a) ₹240 (b) ₹220 (c) ₹1980 (d) ₹182
33. 33.₹66 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹6 (b) ₹33 (c) ₹24 (d) ₹42
34. 34.7 workers can build a wall in 10 days. How many days will 5 workers take, working at the same speed? (a) 15 days (b) 8 days (c) 14 days (d) 12 days
35. 35.4 workers can build a wall in 5 days. How many days will 10 workers take, working at the same speed? (a) 1 day (b) 11 days (c) 3 days (d) 2 days
36. 36.7 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 8 days (b) 6 days (c) 7 days (d) 11 days
37. 37.If 8 pens cost ₹192, how much do 9 pens cost? (a) ₹240 (b) ₹216 (c) ₹193 (d) ₹1728
38. 38.If 5 pens cost ₹80, how much do 4 pens cost? (a) ₹79 (b) ₹80 (c) ₹320 (d) ₹64
39. 39.If 8 kites cost ₹96, how much do 3 kites cost? (a) ₹91 (b) ₹36 (c) ₹288 (d) ₹48
40. 40.If 3 notebooks cost ₹12, how much do 4 notebooks cost? (a) ₹20 (b) ₹48 (c) ₹16 (d) ₹13

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