# If a : b = 2 : 3, a : c = 3 : 4 and b : d = 5 : 2, find c : d. A. 1 : 5 B. 16 : 45 C. 10 : 3 D. 20 : 9 E. 5 : 1

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llltkl | Student

`a : b = 2 : 3, a : c = 3 : 4` and `b : d = 5 : 2`

So, `a/b=2/3` ............(i)

`a/c=3/4 ` ..........(ii)

`b/d=5/2..` ............(iii)

Multiplying (i) and (iii) we get:

`a/b*b/d=2/3*5/2`

`rArr a/d=5/3 ` ..............(iv)

Now, dividing (iv) by (ii) we get:

`a/d*c/a=5/3*4/3`

`rArr c/d=20/9`

Hence, `c:d=20:9`

Therefore, the correct answer is option **D**.