Ratio and proportion

1. Simplify 24:36 to its simplest whole-number form.

Answer A: 2:3

The highest common factor is 12. Dividing both entries by 12 gives 2:3, in the original order.

2. Simplify 15:25:35 to its simplest whole-number form.

Answer C: 3:5:7

All three entries share a factor of 5. Dividing each by 5 gives 3:5:7, with no further common factor.

3. Simplify the ratio 1.5 m:60 cm.

Answer B: 5:2

1.5 m is 150 cm. The ratio is 150:60, and dividing both entries by 30 gives 5:2.

4. Simplify 0.6:1.5 to whole numbers in simplest form.

Answer D: 2:5

Multiplying by 10 gives 6:15. Dividing both entries by 3 then gives the simplest ratio 2:5.

5. Simplify (1/2):(3/4) to whole numbers in simplest form.

Answer A: 2:3

Multiplying each entry by 4 gives 2:3. The same multiplier acts on both fractions, preserving their comparison.

6. A bag contains only red and blue counters in ratio red:blue = 3:5. What fraction of all counters is red?

Answer C: 3/8

There are 3 + 5 = 8 equal parts in total. Red accounts for three of them, so its fraction of the whole is 3/8.

7. MVR 72 is shared between Ali and Bina in ratio 5:3. How much does Ali receive?

Answer B: MVR 45

One part is MVR 72 ÷ 8 = MVR 9. Ali has five parts, so receives MVR 45; Bina receives MVR 27.

8. Share 180 g between A, B and C in ratio 2:3:4. How much does C receive?

Answer D: 80 g

The entries sum to 9, so one part is 180 ÷ 9 = 20 g. C receives 4 × 20 = 80 g.

9. A:B = 4:7. If A = 28, what is B?

Answer A: 49

Four parts equal 28, so one part equals 7. B has seven parts and is therefore 7 × 7 = 49.

10. Small:large = 3:8 for two positive quantities. The large quantity is 64. What is their total?

Answer C: 88

Eight parts equal 64, so one part is 8. The small quantity is 3 × 8 = 24 and their total is 24 + 64 = 88.

11. Two lengths are in ratio longer:shorter = 5:2. Their difference is 21 cm. Find the longer length.

Answer B: 35 cm

The difference of the entries is 5 − 2 = 3. One part is 21 ÷ 3 = 7 cm, so the longer length is 35 cm.

12. A recipe uses 240 g of rice for 6 equal servings. How much rice is needed for 15 equal servings?

Answer D: 600 g

Each serving requires 240 ÷ 6 = 40 g. Fifteen servings require 15 × 40 = 600 g, assuming the same portion size.

13. A recipe uses 450 ml of milk for 9 equal servings. How much is needed for 4 equal servings?

Answer A: 200 ml

One serving needs 450 ÷ 9 = 50 ml. Four equal servings therefore need 4 × 50 = 200 ml.

14. Concentrate:water = 2:7. A drink contains only these ingredients and totals 1.8 litres. How much concentrate is used?

Answer C: 0.4 litres

One part is 1.8 ÷ 9 = 0.2 litres. Concentrate accounts for two parts, so it is 0.4 litres; water is 1.4 litres.

15. On a map of scale 1:25 000, a distance is 6 cm. What actual distance does this represent?

Answer B: 1.5 km

The real distance is 6 × 25 000 = 150 000 cm. There are 100 000 cm in one kilometre, so the answer is 1.5 km.

16. A real distance is 3 km. What is its length on a map with scale 1:50 000?

Answer D: 6 cm

3 km = 300 000 cm. Dividing by 50 000 gives a map length of 6 cm. Multiplying 6 cm back by the scale checks the result.

17. For the same-quality product with no extra charges, which pack has the lowest price per gram? A: 400 g for MVR 32; B: 750 g for MVR 54; C: 1 000 g for MVR 75; D: 250 g for MVR 20.

Answer B: Pack B

The costs per 100 g are MVR 8, MVR 7.20, MVR 7.50 and MVR 8 respectively. Pack B has the lowest unit price.

18. Five identical pens cost MVR 45 at a constant price per pen, with no extra charge. What do eight pens cost?

Answer C: MVR 72

One pen costs MVR 45 ÷ 5 = MVR 9. Eight pens cost 8 × 9 = MVR 72 because the unit price is constant.

19. Which rule preserves the positive ratio 3:5 for every positive scale factor k?

Answer D: Multiply both entries by k

The ratio 3k:5k simplifies back to 3:5 by dividing both entries by k. Adding or subtracting the same amount does not generally preserve it.

20. A:B = 2:3 and B:C = 4:5. Find A:B:C in simplest whole-number form.

Answer A: 8:12:15

Multiply 2:3 by 4 to get 8:12, and 4:5 by 3 to get 12:15. The shared B value is 12, giving A:B:C = 8:12:15.

21. A necklace has only red and blue beads in ratio 2:3. There are 30 beads. If 6 red beads are added and no blue beads change, what is the new red:blue ratio in simplest form?

Answer C: 1:1

Initially red = 30 × 2/5 = 12 and blue = 18. Adding six red beads gives 18 red and 18 blue, hence 1:1.

22. Two positive amounts are in ratio A:B = 4:9. B exceeds A by MVR 65. What is their combined total?

Answer B: MVR 169

One part is MVR 65 ÷ 5 = MVR 13. The total is thirteen parts, so it is 13 × 13 = MVR 169.

23. A delivery costs MVR 20 plus MVR 8 per item. What is the total cost for five items?

Answer D: MVR 60

Five items cost 5 × 8 = MVR 40, plus the one fixed charge of MVR 20. The total is MVR 60; total cost is not proportional to item count.

24. Can 35 indivisible counters be split exactly into two groups in ratio 3:5, with none left over?

Answer A: No; one ratio part would be 35/8 counters

The entries sum to 8. One part would be 35/8, giving non-integer shares 105/8 and 175/8. None of the proposed integer pairs has ratio 3:5, so an exact split is impossible.