Question

three boys are aged 10 years, 12 years and 16 years. They want to divide Rs. 4560 in the ratio of their ages. How much money did each get?

Answer 1

Let the money that first boy get be 10a
Second boy get 12a
Third boy get 16a

According to question
10a+12a+16a = 4560
=> 38a = 4560
=> a = 120

First boy get Rs 1200
Second boy get Rs 1440
Third boy get Rs 1920

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{ \mathfrak{ \: \: Given, \: \: }} \\ \\ \text{The ages are : \red{10 years, 12 years and 16 years}.} \\ \\ \text{Amount of money to be divided = \red{Rs. 4560}} \\ \\ \underline{ \mathfrak{ \: \:To \: \: find : \to \: }} \\ \\ \: \: \: \: \: \: \text{ Part of each each boys = ?}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{As \: \: the \: \: ages \: \: are \: \: 10 \: years, 12 \: years \: \: and \: \: 16 \:} \\ \sf{ years, \: the \: \: ratio \: \: of \: \: their \: \: ages \: \: is = 10 : 12 : 16 } \\ \\ \sf{ \therefore \: Sum \: \: of \: \: the \: \: ratio = \red{10 + 12 + 16} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{\red{= 38}}$

$\tt{ \therefore \: \: Part \: \: of \: \: the \: \: 1st \: \: boy \: \: whose \: \: age \: \: is \: \: } \\ \: \: \: \: \: \: \: \: \tt{ 10 \: years =\pink{Rs.( \frac{10}{38} \times 4560) }}\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ = \red{Rs. \:1200 }}$

$: \leadsto : \tt{ \: \: Part \: \: of \: \: the \: \: 2nd\: \: boy \: \: whose \: \: age \: \: is \: \: } \\ \: \: \: \: \: \: \: \: \tt{ 12 \: years =\pink{Rs.( \frac{12}{38} \times 4560)}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ =\red{Rs. \:1440 }}$

$: \leadsto : \tt{ \: \: Part \: \: of \: \: the \: \: 3rd \: \: boy \: \: whose \: \: age \: \: is \: \: } \\ \: \: \: \: \: \: \: \: \tt{ 16 \: years =\pink{Rs.( \frac{16}{38} \times 4560)}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt{ =\red{Rs. \:1920 }}$