Question

Sum of ages of A and B is 60. 3 years ago ratio of their ages were 4:5. What is the ratio of their ages now??

Answer 1

before three years let the age of A and B be 4x and 5x respectively

4x+3 + 5x+3 = 60

9x+6 =60

9x =60-6

9x =54

x =54/9

x =6

putting value of x

4x + 3 : 5x + 3

4×6+3 : 5×6+3

24+3 : 30+3

27 : 33

therefore 27;33 is the ratio

Answer 2

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{Ratio \ of \ their \ ages \ now \ is \ 27:33.}$

$\sf\orange{\underline{\underline{Given:}}}$

$\sf{\implies{Sum \ of \ ages \ of \ A \ and \ B}}$

$\sf{is \ 60.}$

$\sf{\implies{3 \ years \ ago \ ratio \ of \ their \ ages}}$

$\sf{were \ 4:5.}$

$\sf\pink{\underline{\underline{To \ find:}}}$

$\sf{Ratio \ of \ their \ ages \ now.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ age \ of \ A \ be \ x \ years \ and \ age}$

$\sf{of \ B \ be \ y \ years.}$

$\sf{According \ to \ first \ condition.}$

$\sf{\implies{x+y=60...(1)}}$

$\sf{According \ to \ second \ condition.}$

$\sf{\frac{x-3}{y-3}=\frac{4}{5}}$

$\sf{\therefore{5(x-3)=4(y-3)}}$

$\sf{\therefore{5x-15=4y-12}}$

$\sf{\therefore{5x-4y=-12+15}}$

$\sf{\implies{5x-4y=3…(2)}}$

$\sf{Multiply \ equation \ (1) \ by \ 4 \ throughout,}$

$\sf{\implies{4x+4y=240...(3)}}$

$\sf{Add \ equations \ (3) \ and \ (2)}$

$\sf{4x+4y=240}$

$\sf{+}$

$\sf{5x-4y=3}$

____________________

$\sf{9x=243}$

$\sf{x=\frac{243}{9}}$

$\sf{\implies{x=27}}$

$\sf{Substitute \ x=27 \ in \ equation \ (1)}$

$\sf{27+y=60}$

$\sf{y=60-27}$

$\sf{\implies{y=33}}$

$\sf{\therefore{Age \ of \ A=27 \ years}}$

$\sf{\therefore{Age \ of \ B=33 \ years}}$

$\sf{\frac{A}{B}=\frac{27}{33}}$

$\sf\purple{\tt{\therefore{Ratio \ of \ their \ ages \ now \ is \ 27:33.}}}$