Question

Present ages of Neha and Sana are in the ratio 4:5. Eight years from now the ratio of their
ages will be 5:6. Find their present ages.​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer-}}}}$

The present ages are -

• Neha = 32 years
• Sana = 40 years

$\mathfrak{\large{\underline{\underline{Step-by-step \:explanation-}}}}$

Given :

Present age Ratio = 4 : 5

Ratio of ages after 8 years = 5 : 6

To find :

Their present ages

Solution :

✯ $\textsf{\underline{\underline{Let the present ages be - }}}$

• Neha as 4y
• Sana as 5y

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Ages after 8 years -}}}$

• Neha = 4y + 8
• Sana = 5y + 8

$\bigstar \:\boxed{\sf{ \frac{4y + 8}{5y + 8} = \frac{5}{6}}}$

$\sf{\implies} \: \dfrac{4y + 8}{5y + 8} = \dfrac{5}{6} \\ \\ \sf{\implies} \: 6(4y + 8) = 5(5y + 8) \\ \\ \sf{\implies} \: 24y + 48 = 25y + 40 \\ \\ \sf{\implies} \: 25y - 24y = 48 - 40 \\ \\ \sf{\implies} \: y = 8$

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Neha's present age -}}}$

$\sf{\implies} \: 4(8) \\ \\ \sf{\implies} \: 32$

Neha is presently 32 years old.

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Sana's present age - }}}$

$\sf{\implies} \: 5(8) \\ \\ \sf{\implies} \: 40$

Sana is presently 40 years old.

$\therefore$ The present ages are -

• Neha = 32 years
• Sana = 40 years

Answer 2

$\bold{\underline{\underline{\huge{\tt{AnsWer:}}}}}$

Present age of Neha is 32 years

Present age of Sana is 40 years

$\bold{\underline{\underline{\large{\tt{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• Present ages of Neha and Sana are in the ratio 4:5.
• Eight years from now the ratio of their ages will be 5:6.

To FiNd :

• Their present ages

SoLuTioN :

Let the common multiple of the ratio of present ages be x.

$\tt{\therefore{Respective\:present\:age\:are:}}$

• Neha = 4x years
• Sana = 5x years

$\tt{\underline{\underline{As\:per\:the\:question:}}}$

$\bold{\underline{\tt{\red{Ages\:after\:8\:years:}}}}$

• Neha = 4x + 8 years
• Sana = 5x + 8 years
• Ratio = 5:6

$\leadsto$ $\tt{\dfrac{4x\:+\:8}{5x+8}}$ = $\tt{\dfrac{5}{6}}$

$\leadsto$ $\tt{6(4x+8)\:=\:5(5x+8)}$

$\leadsto$ $\tt{24x+48=25x+40}$

$\leadsto$ $\tt{48-40=25x-24x}$

$\leadsto$ $\tt{8=x}$

Substitute x = 8 in the ratio of ages.

$\bold{\underline{\green{\tt{Present\:age\:of\:Neha:}}}}$

$\leadsto$ $\tt{4x}$

$\leadsto$ $\tt{4\:\times\:8}$

$\leadsto$ $\tt{32}$

$\bold{\boxed{\therefore{\tt{Present\:age\:of\:Neha\:=\:32\:years}}}}$

$\bold{\underline{\purple{\tt{Present\:age\:of\:Sana:}}}}$

$\leadsto$ $\tt{5x}$

$\leadsto$ $\tt{5\:\times\:8}$

$\leadsto$ $\tt{40}$

$\bold{\boxed{\therefore{\tt{Present\:age\:of\:Sana\:=\:40\:years}}}}$