Question

Ages of A and B are in the ratio of 5:4. After 5years the sum of ages becomes 100. Find ages of A and B.

Answer 1

Answer:

Given

A:B =5:4

Let A=5x

B=4x

(A+5)+(B+5)=100

A+B+10=100

A+B=100-10

A+B=90

5x+4x=90

9x=90

x= 90/9

x=10

A= 5x =5×10= 50

B= 4x =4×10= 40

Answer 2

AnswEr :

$\normalsize\bullet\:\sf\ Let \: the \: present \: age \: of \: A \: be \: 5x \: years$

$\normalsize\bullet\:\sf\ Let \: the \: present \: age \: of \: B \: be \: 4x \: years$

$\underline{\dag\:\textsf{According \: to \: the \: question \: now:}}$

$\underline\textsf{After \: 5 \: years:}$

$\normalsize\ : \implies\sf\ (Age \: of \: A + 5) + (Age \: of \: B + 5) = 100 \\ \\ \normalsize\ : \implies\sf\ (5x + 5) + (4x + 5) = 100 \\ \\ \normalsize\ : \implies\sf\ 9x + 10 = 100 \\ \\ \normalsize\ : \implies\sf\ 9x = 90 \\ \\ \normalsize\ : \implies\sf\ x = \frac{\cancel{90}}{\cancel{9}} \\ \\ \normalsize\ : \implies\sf\ x = 10$

$\rule{100}2$

$\normalsize\star\:\sf\ Present \: Age \: of \: A :-$

$\normalsize\ : \implies\sf\ Age_{A} = 5x = 5 \times\ 10 \\ \\ \normalsize\ : \implies\sf\ Age_{A} = 50$

$\normalsize\ : \implies{\underline{\boxed{\sf{Present \: age \: of \: A = 50 \: years}}}}$

$\normalsize\star\:\sf\ Present \: Age \: of \: B :-$

$\normalsize\ : \implies\sf\ Age_{B} = 4x = 4 \times\ 10 \\ \\ \normalsize\ : \implies\sf\ Age_{B} = 40$

$\normalsize\ : \implies{\underline{\boxed{\sf{Present \: age \: of \: B = 40 \: years}}}}$