Question

The ratio of age between $A$ and $B$ is $6:5$ and the age of each $C$ and $D$ is $\frac{9}{10}$ times that of $B$. Age of $F$ is less than $A$ but greater than $B$. The ratio of ages between $B$ and $E$ is $2:3$. Also age of $A$ is $3$ years less than $E$. What is the ratio of ages of $A$ and $F$ if all the ages are in integers?

• A. $12:11$
• B. $9:7$
• C. $24:19$
• D. $12:13$

Answer 1

The correct option is A $12:11$

A= age of A,
= age of B,
= age of C,
= age of D,
= age of E, and
= age of F.
We can use the ratios to calculate , , , and in terms of :
The ratio of the ages ofA:B=6:5. ---> -->-->
The age of each C and D is 9/10 times that Of B. ---> .

The ratio of age of B&E is 2:3. ---> -->-->--> .
For all those ages to be integers, must be a multiple of and ,
so it must be a multiple of .

We can use "guess and check" from here, trying 12, 24, 36, etc as values for .
We can also say that for some whole number ,
and express everyone's age as a function of :
,
,
, and

The age of A is 3 years less than E. ---> -->-->-->--> .
So,
and .
Since the age of F is less than A but greater than B, ,
and the rati we need is

A/B=12/11