If a:b is 2:3, b:c is 4:5 and c:d is 6:7, find the ratio of a:b:c:d

The standard approach in a question on bridging ratios is to find a common element to bridge two ratios.

For example, to bridge a:b and b:c and get a:b:c, ‘b’ is the common element. We make the common element equal so that we can bridge the ratios; this can be done by taking the LCM of the ‘b’ values in both the ratios. This principle holds true whenever you are bridging ratios.

a:b = 2:3 and b:c = 4:5. The LCM of 3 and 4 is 12; hence we multiply the first ratio by 4 and the second by 3 so that ‘b’ becomes the same on both. So, a:b = 8:12 and b:c = 12:15. Now that ‘b’ is common, we can bridge the ratios.
a:b:c = 8:12:15.

Now, to obtain a:b:c:d, we bridge a:b:c with c:d, keeping ‘c’ as the common element. LCM of 15 and 6 is 30; multiply a:b:c by 2 and c:d by 5 to get c=30 on both, then bridge both.

a:b:c = 16:24:30 and c:d = 30:35. Bridging, a:b:c:d = 16:24:30:35.

The correct answer option is E.

An alternative approach would be take actual numbers which are in the respective ratios, identify the common multiples and then bridge the ratio. However, under a time constraint, this may cause errors and hence, I’d recommend the method that we just used to solve this question.

Hope that helps!