**1. An alloy consists of 27 ½ kg of copper and 2 ¾ kg of tin. Find out the ratio by weight of tin to the alloy.**

**Solution:**

**2 Find out the compounded ratio of:**

**(i) 2: 3 and 4: 9**

**(ii) 4: 5, 5: 7 and 9: 11**

**(iii) (a – b): (a + b),(a + b)**

^{2}∶ (a^{2}+ b^{2}) and (a^{4}– b^{4}): (a^{2}– b^{2})^{2}**Solution:**

**3. Find out the duplicate ratio of**

**(i) 2: 3**

**(ii) √5: 7**

**(iii) 5a: 6b**

**Solution:**

^{2}: 3

^{2}= 4: 9

^{2}∶ 7

^{2}= 5: 49

^{2}∶ (6b)

^{2}= 25a

^{2}∶ 36b

^{2}

**4. Find out the triplicate ratio of**

**(i) 3: 4**

**(ii) ½: 1/3**

**(iii) 1**

^{3}∶ 2^{3}**Solution:**

**5. Find out the sub-duplicate ratio of**

**(i) 9: 16**

**(ii) ¼: 1/9**

**(iii)9a**

^{2}∶ 49b^{2}**Solution:**

_{³}

^{2}: 49b

^{2 }

^{2}∶ 49b

^{2}= √9a

^{2}∶ √49b

^{2}= 3a: 7b

**6. Find out the sub-triplicate ratio of**

**(i) 1: 216**

**(ii) 1/8: 1/125**

**(iii)27a**

^{3}∶ 64b^{3}**Solution:**

^{3})

^{(1/3)}∶ (6

^{3})

^{(1/3)}

**7. Find out the reciprocal ratio of**

**(i) 4: 7**

**(ii) 3**

^{2}∶ 4^{2}**(iii) 1/9: 2**

**Solution:**

^{2}∶ 4^2

^{2}∶ 4

^{2}= 4

^{2}∶ 3

^{2}= 16: 9

**8. Arrange the following ratios in ascending order of magnitude:**

**2: 3,17: 21,11: 14 and 5: 7**

**Solution:**

**9. (i) If A: B = 2: 3,B: C = 4: 5 and C: D = 6: 7,find A: D.**

**(ii) If x: y = 2: 3 and y: z = 4: 7,find x: y: z.**

**Solution:**

**10. (i) If A: B = 1/4: 1/5 and B: C = 1/7: 1/6,find A: B: C.**

**(ii) If 3A = 4B = 6C,find A: B: C**

**Solution:**

**11. (i) If 3x + 5y/ 3x – 5y = 7/3,find x: y.**

**(ii) If a: b = 3: 11,find (15a – 3b): (9a + 5b).**

**Solution:**

**13. (i) If (x – 9): (3x + 6) is the duplicate ratio of 4: 9, Find out the value of x.**

**(ii) If (3x + 1): (5x + 3) is the triplicate ratio of 3: 4, Find out the value of x.**

**(iii) If (x + 2y): (2x – y) is equal to the duplicate ratio of 3: 2, Find out x: y.**

**Solution:**

**14. (i) Find out two numbers in the ratio of 8: 7 such that when each is decreased by 12 ½, they are in the ratio 11: 9.**

**(ii) The income of a man is increased in the ratio of 10: 11. If the increase in his income is Rs 600 per month, Find out**

**Solution :**

**15. (i) A woman reduces her weight in the ratio 7: 5. What does her weight become if originally it was 91 kg.**

**(ii) A school collected Rs 2100 for charity. It was decided to divide the money between an orphanage and a blind school in the ratio of 3: 4. How much money did each receive?**

**Solution:**

**16. (i) The sides of a triangle are in the ratio 7: 5: 3 and its perimeter is 30 cm. Find out the lengths of sides.**

**(ii) If the angles of a triangle are in the ratio 2: 3: 4, Find out the angles.**

**Solution:**

**17. Three numbers are in the ratio 1/2: 1/3: ¼. If the sum of their squares is 244, Find out the numbers.**

**Solution:**

^{2}+ (4x)

^{2}+ (3x)

^{2}= 244

^{2 }+ 16x

^{2}+ 9x

^{2}= 244

^{2 }= 244

^{2}= 244/61 = 4 = 2

^{2}

**18. (i) A certain sum was divided among A, B and C in the ratio 7: 5: 4. If B got Rs 500 more than C, Find out the total sum divided.**

**(ii) In a business, A invests Rs 50000 for 6 months, B Rs 60000 for 4 months and C Rs 80000 for 5 months. If they together earn Rs 18800 Find out the share of each.**

**Solution:**