# Mohammad's height is 169cm and Fatima's 'ht. is 156cm.The frame sizes of their bikes are in the same ratio as their hts.The frame size of Muhammed's bike is 52cm.Calculate the frame size of...

Mohammad's height is 169cm and Fatima's 'ht. is 156cm.The frame sizes of their bikes are in the same ratio as their hts.

The frame size of Muhammed's bike is 52cm.Calculate the frame size of Fatima's bike.

hala718 | Certified Educator

Let Mohammed's height be Mb = 169

And let Fatima's height be Fh = 156

Also, given Mohammeds bike (Mb) = 52

Then have the same ration for their bikes:

==> we will rewrite:

Mh = 169   ==>   Mb = 52

Fh = 156  ==>    Fb = ?

Now since they have the same ratio, then we will cross multiply:

==> 169*Fb = 52* 156

==> Fb = 52*156/ 169

==> Fb = 48

Then Fatima's bike height is 48

justaguide | Certified Educator

We have to use ratios here. We are given that Mohammad's height is 169 cm and his bike's frame size is 52 cm. Let the ratio of height to frame size be S.

So S = 169 / 52.

Now Fatima's height is 156 cm. Let her frame size be D.

So S = 156 / D

Now as the ratio of of height to frame size is the same

S = 169 / 52 = 156 / D

=> D = 156 * 52 / 169 = 48.

The required frame size of Fatima's bike is 48.