If x:y = 3:4 and y:z = 8:9, z:a is 15:16, find x:y:z:a (a) 30:40:45: 48 (b) 78:82:65:45 (c) 76:90:56:80 (d) None of these Options : a b c d

To solve this problem, we need to find a common multiplier for each ratio to link them together.

1. Start with the given ratios: x:y = 3:4, y:z = 8:9, and z:a = 15:16.

2. Notice that 'y' in the first ratio can be linked with 'y' in the second ratio if we multiply the first ratio by 2. This gives us x:y = 6:8.

3. Now, 'z' in the second ratio can be linked with 'z' in the third ratio if we multiply the second ratio by 15. This gives us y:z = 120:135.

4. But now 'y' in the first ratio (6:8) doesn't match with 'y' in the second ratio (120:135). To match them, we can multiply the first ratio by 20, giving us x:y = 120:160.

5. Now 'y' in the first ratio matches with 'y' in the second ratio. So we can link these two ratios together to get x:y:z = 120:160:135.

6. Finally, we can link the third ratio (z:a = 15:16) with the combined ratio by multiplying the third ratio by 9, giving us z:a = 135:144.

7. Now 'z' in the combined ratio matches with 'z' in the third ratio. So we can link these ratios together to get the final combined ratio x:y:z:a = 120:160:135:144.

So, the answer is (d) None of these.