Question

The ratio of the number of marbles with Ram and Shyam is 19 : 13. If Ram gives Shyam 30 marbles, both will have equal number of marbles. Find the number of marbles with Ram​

Answer 1

-------------------------------

▪ Given :-

• The ratio of the number of marbles with Ram and Shyam is 19 : 13

• If Ram gives Shyam 30 marbles, both will have equal number of marbles

-------------------------------

▪ To Find :-

• The number of marbles with Ram.

-------------------------------

▪ Solution :-

$\large \bigstar \:   \underline{ \pmb{ \mathfrak{ Let,}}}$

• No. of marbles with Ram = 19 x

Hence,

• No. of marbles with Shyam = 13 x.

《When Ram gives Shyam 30 marbles》

• No. of marbles with Ram = 19x - 30

• No. of marbles with Shyam = 13x + 30

$\large \bigstar \:\underline{ \pmb{ \mathfrak{ \text{A}ccording \:to \:the \:Given \:Condition}}}$

$\sf1 9 \mathtt x - 30 = 13\mathtt x + 30 \\ \\ :\longmapsto \sf19\mathtt x - 13\mathtt x = 30 + 30 \\ \\ :\longmapsto \sf6\mathtt x = 60 \\ \\ \mathtt x = \cancel{ \frac{60}{6} }\\ \\ \Large\purple{:\longmapsto  \underline {\boxed{{\bf x = 10} }}}$

Hence ,

$\large \pink{\pmb{ \mathfrak{\text{N}umber \: of \: marbles \: with \: Ram = } \: 190}}$

$\Large \red{\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer.}}$

-------------------------------

Answer 2

Let

Number of marbles with Ram = 19 x

Accordingly

Number of marbles with Shyam = 13 x.

When Ram gives Shyam 30 marbles :

Number of marbles with Ram = 19x - 30

Number of marbles with Shyam 13x + 30

According To Question :

$\bf1 9 x - 30 = 13 x + 30 \\ \\ :\implies \bf19 x - 13 x = 30 + 30 \\ \\ :\implies \bf6 x = 60 \\ \\ \mathfrak{ \:\implies  \underline {{{\bf x = 10} }}}$

$\underline{\pmb{ \mathfrak{Number \: of \: marbles \: with \: Ram = } \: 190}}$