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 theseOptions :abcd

To solve this problem, we need to find a common multiplier for y in the ratios x:y and y:z, and for z in the ratios y:z and z:a.

1. In the ratio x:y = 3:4, y is 4.
2. In the ratio y:z = 8:9, y is 8.

The least common multiple of 4 and 8 is 8. So, we multiply the first ratio by 2 to make y the same in both ratios. We get x:y = 6:8.

3. In the ratio y:z = 8:9, z is 9.
4. In the ratio z:a = 15:16, z is 15.

The least common multiple of 9 and 15 is 45. So, we multiply the second ratio by 5 and the third ratio by 3 to make z the same in both ratios. We get y:z = 40:45 and z:a = 45:48.

So, the combined ratio x:y:z:a is 6:8:40:45:45:48, which simplifies to 6:40:45:48.

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