Question

The age of A and B are in the ratio 1:2. After 8 years their ages will be in the ratio 3:4. Their present age is ________ ​

Answer 1

Answer:

12 and 16 will be their present age

Step-by-step explanation:

i think its right.

neglect - before 4 cause we can't take - 8n ages.

Answer 2

$\mathfrak{{\pmb{{\underline{Given}}:}}}$

• The ages of A and B are in the ratio $\sf{\pmb{1:2}}$
• After 8 years their ages will be in the ratio $\sf{\pmb{3:4}}$

$\mathfrak{{\pmb{{\underline{To~find}}:}}}$

• The present ages of A and B

$\mathfrak{{\pmb{{\underline{Solution}}:}}}$

• Let the ratios of the present ages of A and B be, 1x and 2x
• After 8 years, the ratio becomes $\sf{\pmb{3:4}}$

$\sf{~~~~~~~~~~ (1x+8):(2x+8)=3:4}$

$\sf\implies{{\dfrac{x+8}{2x+8}}={\dfrac{3}{4}}}$

$\sf{\pmb{Cross~multiplying,~we~get:}}$

$\sf\implies{4(x+8)=3(2x+8)}$

$\sf\implies{4x+32=6x+24}$

$\sf\implies{4x-6x=24-32}$

$\sf\implies{\cancel{-}~2x=\cancel{-}~8}$

$\sf\implies{2x=8}$

$\sf\implies{x={\dfrac{8}{2}}}$

$\sf{~~~~~~~ {\blue{•~{\underline{\boxed{\sf{\pmb{x=4}}}}}}}}$

$\therefore\mathfrak{{\pmb{{\underline{Required~answer}}:}}}$

Present age of A = 1x = $\sf{\pmb{4~years}}$

Present age of B = 2x = $\sf{2×4={\pmb{8~years}}}$