Question 979941
let's Rohit's age be {{{x}}} and Rana's age be {{{y}}}

if the ratio of ages of Rohit and Rana is {{{5:7}}}(means Rohit is older), we have

{{{5:7=x:y}}}
or
{{{7x=5y}}}.........solve for {{{x}}}

{{{x=(5/7)y}}}......eq.1

 and if their difference of age is {{{4}}} years, we have

{{{y-x=4}}}................solve for {{{x}}}

{{{x=y-4}}}......eq.2

since left sides of eq.1 and eq.2 are same, than right sides are same too

so, we have

{{{(5/7)y=y-4}}}........solve for {{{y}}}

{{{7(5/7)y=7y-4*7}}}

{{{5y=7y-28}}}

{{{0=7y-5y-28}}}

{{{28=2y}}}

{{{y=28/2}}}

{{{y=14}}}

and

{{{x=y-4}}}=>{{{x=14-4}}}=>{{{x=10}}}


so, the sum their ages is {{{x+y=10+14=24}}}