A basic question from ML aggarwal book of class 10th, ratio and proportion, class 10th 7th chapter

This is very basic ques and important as well

In this question we have been a:b, b:c, c:d,

And we have to calculate d:a

And in second part we have x:y and y:z and we have to find x:y:z

Question no. 9, ML Aggarwal

Solution:(i) It is given that

A: B = 2: 3, B: C = 4: 5 and C: D = 6: 7

We can write it as

A/ B = 2/3, B/C = 4/5, C/D = 6/7

By multiplication

A/B × B/C × C/D = 2/3 × 4/5 × 6/7

So we get

A/D = 16/35

A: D = 16: 35

(ii) We know that the LCM of y terms 3 and 4 is 12

Now making equals of y as 12

x/y = 2/3 = (2 × 4)/ (3 × 4) = 8/12 = 8: 12

y/z = 4/7 × 3/3 = 12/21 = 12: 21

So x: y: z = 8: 12: 21