Question

11. The age of Ruby and Tabassum are in the ratio 5:7.
Five years later, their ages will be in the ratio 3:4.
Find the Tabassum age.
(a) 20 years
(b) 35 years
(c) 30 years
(d) None of these​

Answer 1

Given

$\bold{The \ ages \ of \ Ruby \ and \ Tabassum \ are \ in \ the \ ratio \ 5:7}$

$\implies \bold{Let \ the \ ages \ of \ Ruby \ and \ Tabassum \ be \ 5x \ and \ 7x \ respectively}$

$\bold{Five \ years \ later, \ their \ ages \ will \ be \ in \ the \ ratio \ 3:4}$

$\implies \sf\dfrac{5x+5}{7x+5} = \dfrac{3}{4}$

$\implies \sf 4(5x+5)=3(7x+5)\\ \\\implies \sf 20x+20=21x+15\\\\\implies \sf 20x-21x=15-20\\\\\implies \sf -x=-5\\\\\implies \sf x = 5$

$\bold{Therefore, \ Tabassum's \ age \ will \ be \ 5 \times 7 =\underline{\underline {35 \ years}}}}$

$\boxed{\boxed{\bold{Therefore, \ Option \ b) \ \ is \ your \ answer}}}$

                                                                             

Answer 2

Answer:

ratio of present age=5/7

their ages after 5 yrs=5x+5 yrs/7x+5 yrs=3/4

by cross multiplication

20x+20=21x+15

20x-21x=15-20

-x=-5

x=5

now tabassum's age=7*5=35 yrs