Question

The ages of "Lalloo Prasad" and "Mulayam Singh" are in the ratio of 9:4. After 7 years the ratio will become 5: 3. Find their present ages.​

Answer 1

Answer:

$\frac{9x + 7}{4x + 7} = \frac{5}{3} \\ 27x + 21 = 20x + 35 \\ 7x = 14 \\ x = 2 \\ age \: is \: 18 \: and \: 8$

Answer 2

$\bf \underline{ \underline{\maltese\:Given} }$

$\sf The \: ages \: of \: Lalloo \: Prasad \: and \: Mulayam \: Singh \: are \: in \: the \: ratio \: of \: 9:4.$

$\sf \implies After \: 7 \: years \: the \: ratio \: will \: become \: 5: 3.$

$\bf \underline{ \underline{\maltese \: To \: find } }$

$\sf \implies Their \: present \: ages = \: ?$

$\bf \underline{ \underline{\maltese \: Solution } }$

$\sf Let \: us \: assume \: that,$

$\sf \implies Lalloo \: Prasad's \: age \: be \: 9x$

$\sf \implies Mulayam \: Singh's \: age \: be \: 4x$

$\bf \underline{Now},$

$\sf \implies After \: 7 \: years \: the \: ratio \: will \: become \: 5: 3.$

$\sf \underline{Hence, our \: equation \: will \: be} :$

$\implies\bf \red{\dfrac{(9x +7)}{(4x + 7)} = \dfrac{5}{3} }$

$\sf \underline{Now, we \: will \: solve \: the \: above \: equation. }$

$\sf\implies (9x + 7) \times 3 = (4x + 7) \times 5$

$\sf\implies 27x + 21 = 20x + 35$

$\sf\implies 27x + 21 - 20x = 35$

$\sf\implies 7x + 21 = 35$

$\sf\implies 7x = 35 - 21$

$\sf\implies 7x = 14$

$\sf\implies x = \cancel \dfrac{14}{7}$

$\sf\implies x = 2$

$\bf \underline{Therefore},$

$\sf \implies Lalloo \: Prasad's \: age = \bf 9x = 9 \times 2 = 18 \: years$

$\sf \implies Mulayam \: Singh's \: age = \bf 4x = 4 \times 2 = 8 \:years$