Question

Arnav is thrice as old as his sister. In 10 years from now , the sum of their ages will be 48 years. How old are they now?​

Answer 1

Answer:

Given :-

• Arnav is thrice as old as his sister.
• In 10 years from now, the sum of their ages will be 48 years.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf Present\: Age_{(Arnav's\: Sister)} =\: a\: years$

$\mapsto \bf Present\: Age_{(Arnav)} =\: 3a\: years$

❒ After 10 years their ages will be :

$\leadsto \sf Age_{(Arnav's\: Sister)} =\: (a + 10)\: years$

$\leadsto \sf Age_{(Arnav)} =\: (3a + 10)\: years$

According to the question,

$\bigstar$ After 10 years, their sum of their ages will be 48 years.

$\footnotesize\implies \bf \bigg\{Age_{(Arnav's\: Sister)}\bigg\} + \bigg\{Age_{(Arnav)}\bigg\} =\: \bigg\{48\bigg\}$

$\implies \sf (a + 10) + (3a + 10) =\: 48$

$\implies \sf a + 10 + 3a + 10 =\: 48$

$\implies \sf a + 3a + 10 + 10 =\: 48$

$\implies \sf 4a + 20 =\: 48$

$\implies \sf 4a =\: 48 - 20$

$\implies \sf 4a =\: 28$

$\implies \sf a =\: \dfrac{\cancel{28}}{\cancel{4}}$

$\implies \sf a =\: \dfrac{7}{1}$

$\implies \sf\bold{\purple{a =\: 7}}$

Hence, their required present ages are :

❒ Present Age Of Arnav's Sister :

$\longrightarrow \sf Present\: Age_{(Arnav's\: Sister)} =\: a\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Arnav's\: Sister)} =\: 7\: years}}$

❒ Present Age Of Arnab :

$\longrightarrow \sf Present\: Age_{(Arnav)} =\: 3a\: years$

$\longrightarrow \sf Present\: Age_{(Arnav)} =\: (3 \times 7)\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Arnav)} =\: 21\: years}}$

${\small{\bold{\underline{\therefore\: The\: present\: age\: of\: Arnav\: and\: his\: sister\: is\: 21\: years\: and\: 7\: years\: .}}}}$

Answer 2

Given :-

• Arnav is thrice as old as his sister
• In 10 years, the sum of Arnav and his sister will be 48.

To Find :-

• Present age of Arnav and his sister.

Let :-

• The current age of Arnav's sister be x.
• The current age of Arnav be 3x.

$\sf \red{\therefore According \: to \: the \: question :-}$

• Arnav's age after 10 years = 3x + 10
• His sister's age after 10 years = x + 10

$\sf {Putting\: the\: values \:we\: get :-} \\ \sf {\longrightarrow x + 10 + 3x + 10 = 48 } \: \: \\ \sf {\longrightarrow 4x + 20 = 48 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf {\longrightarrow \: 4x =48 - 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf {\longrightarrow \: 4x = 28 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \\ \sf {\longrightarrow \: x = \frac{ \cancel{28}}{ \cancel{4}} = 7 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$\sf \purple{\therefore Arnav's \: age = 3x = 21 \: \: \: } \\ \sf \blue {and \: his \: sister's \: age \: = x = 7}$