Question

The sum of the present ages of Sita and Rita is 105 years. After 7 years the ratio of their ages that time will be 7 : 10 respectively. What is Rita’s present age ?​

Answer 1

$\large \bf \clubs \: Given :-$

• The sum of the present ages of Sita and Rita is 105 years.

• After 7 years the ratio of their ages that time will be 7 : 10 respectively.

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$\large \bf \clubs \: To \: Find :-$

• Rita’s present age

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$\large \bf \clubs \: Solution :-$

Let ,

• Present age of Sita be = x years

• Present age of Rita be = y years

We Have,

$\sf \mathtt x + y = 105 \\ \\ : \: \bf \large\longmapsto x = 105 - y \: \: - - - - (1)$

《After 7 Years》

• Age of Sita = (x + 7) years

• Age of Rita = (y + 7) years

According To The Given Condition :

$\sf\dfrac{\mathtt x + 7}{y + 7} = \frac{7}{10} \\ \\ :\longmapsto \sf10(\mathtt x + 7) = 7(y + 7) \\ \\ :\longmapsto \sf10\mathtt x + 70 = 7y + 49 \\ \\ \large:\longmapsto \bf10x - 7y = - 21 \: \: - - (2)$

Putting Value of (2) in (1)

$:\longmapsto \sf10(105 - y) - 7y = - 21 \\ \\ :\longmapsto \sf 1050 - 10y - 7y = - 21\\ \\ :\longmapsto \sf \cancel - 17y = \cancel- 1071\\ \\ :\longmapsto \sf y = \frac{1071}{17} \\ \\ \purple{ \Large :\longmapsto  \underline {\boxed{{\bf y = 63} }}}$

$\underline{ \underline{ \pink{ \pmb{Hence \: Present \: Age \: of \: Rita = 63 \: years }}}}$

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

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Answer 2

Let us Assume that

Present age of Sita be = s years

Present age of Rita be = r years

Acc. To Question

$\mathtt{ s+ r = 105} \\ \\ : \: \pmb{ \large\implied d = 105 - r} - - - - (i)$

After 7 Years >>

Age of Sita will be = (s + 7) years

Age of Rita will be = (r + 7) years

Acc. To Question

$\mathtt{\dfrac{\mathtt s + 7}{r + 7} = \frac{7}{10} }\\ \\ :\implies \mathtt{10(\mathtt d + 7) = 7(r + 7) }\\ \\ :\implies \mathtt{10\mathtt s + 70 = 7r + 49} \\ \\ \large:\longmapsto \bf{10s - 7r = - 21}-- - - (ii)$

From Both Equation

$\mathtt{10(105 - r) - 7r= - 21 }\\ \\ :\implies \sf 1050 - 10r- 7r= - 21\\ \\ :\implies \sf - 17r= - 1071\\ \\ :\implies \LARGE\mathfrak{ r = 63}$

So Rita's Age = 63 years