Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 413 · 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 9 mangoes cost ₹108, how much do 12 mangoes cost? (a) ₹1296 (b) ₹111 (c) ₹144 (d) ₹156
2. 2.If 4 kites cost ₹84, how much do 3 kites cost? (a) ₹252 (b) ₹84 (c) ₹63 (d) ₹83
3. 3.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 6 days (c) 4 days (d) 10 days
4. 4.4 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 5 days (c) 18 days (d) 4 days
5. 5.If 2 mangoes cost ₹28, how much do 12 mangoes cost? (a) ₹168 (b) ₹336 (c) ₹182 (d) ₹38
6. 6.If 9 kites cost ₹63, how much do 10 kites cost? (a) ₹70 (b) ₹64 (c) ₹630 (d) ₹77
7. 7.₹350 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹225 (b) ₹125 (c) ₹25 (d) ₹175
8. 8.5 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 17 days
9. 9.If 3 notebooks cost ₹72, how much do 4 notebooks cost? (a) ₹96 (b) ₹288 (c) ₹120 (d) ₹73
10. 10.₹132 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹108 (b) ₹24 (c) ₹12 (d) ₹66
11. 11.₹410 is shared between two friends in the ratio 1 : 9. How much is the bigger share? (a) ₹205 (b) ₹369 (c) ₹41 (d) ₹410
12. 12.If 8 kites cost ₹56, how much do 9 kites cost? (a) ₹504 (b) ₹57 (c) ₹70 (d) ₹63
13. 13.5 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 5 days (c) 11 days (d) 4 days
14. 14.8 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 52 days (c) 19 days (d) 53 days
15. 15.If 5 mangoes cost ₹45, how much do 4 mangoes cost? (a) ₹44 (b) ₹36 (c) ₹180 (d) ₹45
16. 16.₹70 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹10 (b) ₹20 (c) ₹50 (d) ₹35
17. 17.If 5 notebooks cost ₹45, how much do 4 notebooks cost? (a) ₹36 (b) ₹44 (c) ₹180 (d) ₹45
18. 18.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 2 days (b) 3 days (c) 4 days (d) 19 days
19. 19.If 4 notebooks cost ₹32, how much do 8 notebooks cost? (a) ₹64 (b) ₹36 (c) ₹72 (d) ₹256
20. 20.If 8 mangoes cost ₹24, how much do 11 mangoes cost? (a) ₹264 (b) ₹33 (c) ₹27 (d) ₹36
21. 21.If 5 kites cost ₹110, how much do 6 kites cost? (a) ₹111 (b) ₹132 (c) ₹154 (d) ₹660
22. 22.If 4 notebooks cost ₹16, how much do 2 notebooks cost? (a) ₹32 (b) ₹8 (c) ₹14 (d) ₹12
23. 23.9 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 5 days (c) 9 days (d) 45 days
24. 24.5 workers can build a wall in 10 days. How many days will 10 workers take, working at the same speed? (a) 20 days (b) 15 days (c) 6 days (d) 5 days
25. 25.₹125 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹75 (b) ₹25 (c) ₹50 (d) ₹100
26. 26.If 4 pens cost ₹56, how much do 9 pens cost? (a) ₹140 (b) ₹126 (c) ₹504 (d) ₹61
27. 27.9 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 7 days (b) 21 days (c) 63 days (d) 64 days
28. 28.If 9 pens cost ₹81, how much do 8 pens cost? (a) ₹648 (b) ₹81 (c) ₹80 (d) ₹72
29. 29.6 workers can build a wall in 8 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 10 days (c) 7 days (d) 5 days
30. 30.₹253 is shared between two friends in the ratio 5 : 6. How much is the bigger share? (a) ₹115 (b) ₹161 (c) ₹138 (d) ₹23
31. 31.₹108 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹27 (b) ₹54 (c) ₹108 (d) ₹81
32. 32.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 9 days (c) 4 days (d) 6 days
33. 33.If 2 mangoes cost ₹34, how much do 9 mangoes cost? (a) ₹306 (b) ₹170 (c) ₹41 (d) ₹153
34. 34.6 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 6 days (b) 4 days (c) 2 days (d) 3 days
35. 35.If 3 pens cost ₹63, how much do 10 pens cost? (a) ₹630 (b) ₹210 (c) ₹231 (d) ₹70
36. 36.5 workers can build a wall in 14 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 19 days (c) 28 days (d) 7 days
37. 37.If 5 mangoes cost ₹55, how much do 9 mangoes cost? (a) ₹59 (b) ₹110 (c) ₹495 (d) ₹99
38. 38.₹231 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹231 (b) ₹198 (c) ₹33 (d) ₹199
39. 39.If 4 pens cost ₹96, how much do 9 pens cost? (a) ₹101 (b) ₹864 (c) ₹240 (d) ₹216
40. 40.₹40 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹20 (b) ₹16 (c) ₹24 (d) ₹8

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