Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 721 · 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 4 notebooks cost ₹24, how much do 8 notebooks cost? (a) ₹48 (b) ₹28 (c) ₹192 (d) ₹54
2. 2.If 7 pens cost ₹147, how much do 2 pens cost? (a) ₹42 (b) ₹63 (c) ₹142 (d) ₹294
3. 3.3 workers can build a wall in 14 days. How many days will 7 workers take, working at the same speed? (a) 10 days (b) 18 days (c) 7 days (d) 6 days
4. 4.₹500 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹50 (b) ₹150 (c) ₹350 (d) ₹250
5. 5.4 workers can build a wall in 15 days. How many days will 10 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 6 days (d) 7 days
6. 6.6 workers can build a wall in 7 days. How many days will 2 workers take, working at the same speed? (a) 22 days (b) 21 days (c) 11 days (d) 3 days
7. 7.4 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 11 days (b) 27 days (c) 26 days (d) 15 days
8. 8.9 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 10 days (b) 8 days (c) 1 day (d) 9 days
9. 9.3 workers can build a wall in 12 days. How many days will 2 workers take, working at the same speed? (a) 13 days (b) 8 days (c) 11 days (d) 18 days
10. 10.If 9 pens cost ₹144, how much do 7 pens cost? (a) ₹128 (b) ₹1008 (c) ₹112 (d) ₹142
11. 11.If 7 mangoes cost ₹49, how much do 8 mangoes cost? (a) ₹392 (b) ₹63 (c) ₹50 (d) ₹56
12. 12.₹374 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹136 (b) ₹187 (c) ₹34 (d) ₹238
13. 13.₹250 is shared between two friends in the ratio 2 : 3. How much is the bigger share? (a) ₹50 (b) ₹150 (c) ₹100 (d) ₹125
14. 14.If 7 kites cost ₹98, how much do 4 kites cost? (a) ₹95 (b) ₹70 (c) ₹56 (d) ₹392
15. 15.5 workers can build a wall in 8 days. How many days will 10 workers take, working at the same speed? (a) 16 days (b) 3 days (c) 4 days (d) 13 days
16. 16.If 2 pens cost ₹30, how much do 5 pens cost? (a) ₹33 (b) ₹90 (c) ₹75 (d) ₹150
17. 17.₹456 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹38 (b) ₹228 (c) ₹266 (d) ₹190
18. 18.₹238 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹68 (b) ₹119 (c) ₹170 (d) ₹34
19. 19.7 workers can build a wall in 6 days. How many days will 3 workers take, working at the same speed? (a) 14 days (b) 15 days (c) 2 days (d) 10 days
20. 20.5 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) 4 days (d) 11 days
21. 21.₹130 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹65 (b) ₹50 (c) ₹80 (d) ₹10
22. 22.3 workers can build a wall in 4 days. How many days will 12 workers take, working at the same speed? (a) 1 day (b) 16 days (c) 13 days (d) 2 days
23. 23.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 9 days (b) 6 days (c) 4 days (d) 5 days
24. 24.If 6 pens cost ₹114, how much do 5 pens cost? (a) ₹113 (b) ₹114 (c) ₹95 (d) ₹570
25. 25.If 2 pens cost ₹48, how much do 7 pens cost? (a) ₹168 (b) ₹336 (c) ₹192 (d) ₹53
26. 26.₹429 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹78 (b) ₹351 (c) ₹390 (d) ₹39
27. 27.₹104 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹8 (b) ₹32 (c) ₹52 (d) ₹72
28. 28.If 3 pens cost ₹42, how much do 2 pens cost? (a) ₹42 (b) ₹28 (c) ₹84 (d) ₹41
29. 29.If 3 pens cost ₹39, how much do 4 pens cost? (a) ₹156 (b) ₹40 (c) ₹65 (d) ₹52
30. 30.₹420 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹175 (b) ₹210 (c) ₹35 (d) ₹245
31. 31.6 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 15 days (b) 14 days (c) 4 days (d) 10 days
32. 32.If 8 kites cost ₹48, how much do 5 kites cost? (a) ₹45 (b) ₹240 (c) ₹30 (d) ₹36
33. 33.If 3 pens cost ₹63, how much do 8 pens cost? (a) ₹189 (b) ₹168 (c) ₹68 (d) ₹504
34. 34.If 5 notebooks cost ₹125, how much do 9 notebooks cost? (a) ₹225 (b) ₹129 (c) ₹250 (d) ₹1125
35. 35.3 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 3 days (d) 7 days
36. 36.₹360 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹180 (b) ₹225 (c) ₹45 (d) ₹135
37. 37.If 5 notebooks cost ₹115, how much do 3 notebooks cost? (a) ₹345 (b) ₹92 (c) ₹69 (d) ₹113
38. 38.If 7 notebooks cost ₹133, how much do 10 notebooks cost? (a) ₹1330 (b) ₹209 (c) ₹190 (d) ₹136
39. 39.₹380 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹266 (b) ₹114 (c) ₹38 (d) ₹190
40. 40.If 8 pens cost ₹192, how much do 6 pens cost? (a) ₹1152 (b) ₹144 (c) ₹190 (d) ₹168

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