Question

The sum of present Ages of Rohan and Mohan is 105 years after 7 years their ages will be in the ratio 7:10.
Find the present ages of Rohan and mohan

Answer 1

$\large \clubs \:  \bf Given :  -$

• The sum of the present ages of Rohan and Mohan is 105 years.

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

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

• Their Present Ages

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

Let ,

• Present age of Rohan = x years

• Present age of Sohan = y years

✏ We Have,

$\sf \text {x + y = 105 }$

$\bf :\longmapsto x = 105 - y \: \: - - - - (1)$

《After 7 Years》

• Age of Rohan = (x + 7) years

• Age of Mohan = (y + 7) years

✏ According To Question  :

$\sf\dfrac{\text x + 7}{ \text y + 7} = \frac{7}{10}$

$:\longmapsto \sf10( \text{ x + 7) = 7(y + 7)}$

$:\longmapsto \sf10\text{x + 70 = 7y + 49 }$

$:\longmapsto \bf10x - 7y = - 21 \: \: - - - - (2)$

✏ Putting Value of (1) in (2) :

$:\longmapsto10(105 -\text y) - 7\text y = - 21$

$:\longmapsto1050 - 10\text y - 7\text y = - 21$

$:\longmapsto - 17\text y = - 21 - 1050$

$:\longmapsto \cancel- 17\text y = \cancel- 1071$

$:\longmapsto\text y = \cancel \dfrac{1071}{17}$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf y = 63} }}}$

✏ Putting Value of y in (1) :

$:\longmapsto\text x = 105 - 63$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf x = 42} }}}$

Hence,

$\pink{\begin{cases} \bf Age \: of \: Rohan = 42 \: years \\ \\ \bf Age \: of \: Mohan = 63 \:years\end{cases}}$

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Answer 2

Answer:

Given :-

• The sum of present age of Rohan and Mohan is 105.
• After 7 years their ages will be in the ratio of 7 : 10.

To Find :-

• What is the present age of Rohan and Mohan.

Solution :-

Let,

$\mapsto \bf Present\: Age\: of\: Rohan =\: a\: years$

$\mapsto \bf Present\: Age\: of\: Mohan =\: b\: years$

Now,

$\bigstar$ Sum of present age of Rohan and Mohan is 105.

$\implies \sf a + b =\: 105$

$\implies \sf\bold{\purple{a =\: 105 - b\: ------\: (Equation\: No\: 1)}}$

Again,

$\bigstar$ After 7 years their ages will be :

$\leadsto \sf Age\: of\: Rohan =\: (a + 7)\: years$

$\leadsto \sf Age\: of\: Mohan =\: (b + 7)\: years$

$\bigstar$ After 7 years their ages will be in the ratio of 7 : 10.

$\implies \bf (a + 7) : (b + 7) =\: 7 : 10$

$\implies \sf \dfrac{(a + 7)}{(b + 7)} =\: \dfrac{7}{10}$

By doing cross multiplication we get,

$\implies \sf 7(b + 7) =\: 10(a + 7)$

$\implies \sf 7b + 49 =\: 10a + 70$

$\implies \sf 7b - 10a =\: 70 - 49$

$\implies \sf\bold{\purple{7b - 10a =\: 21\: ------\: (Equation\: No\: 2)}}$

Now, by putting the value of a in the equation no 2 we get,

$\implies \sf 7b - 10a =\: 21$

$\implies \sf 7b - 10\{105 - b\} =\: 21$

$\implies \sf 7b - 1050 + 10b =\: 21$

$\implies \sf 7b + 10b =\: 21 + 1050$

$\implies \sf 17b =\: 1071$

$\implies \sf b =\: \dfrac{\cancel{1071}}{\cancel{17}}$

$\implies \sf b =\: \dfrac{63}{1}$

$\implies \sf\bold{\pink{b =\: 63}}$

Again, by putting b = 63, in the equation no 1 we get,

$\implies \sf a =\: 105 - b$

$\implies \sf a =\: 105 - 63$

$\implies \sf\bold{\pink{a =\: 42}}$

Hence, we get the required present age of Rohan and Mohan is :

$\longrightarrow \tt\bold{\red{Present\: Age_{(Rohan)} =\: 42\: years}}$

$\longrightarrow \tt\bold{\red{Present\: Age_{(Mohan)} =\: 63\: years}}$

${\small{\bold{\underline{\therefore\: The\: present\: age\: of\: Rohan\: and\: Mohan\: are\: 42\: years\: and\: 63\: years\: respectively\: .}}}}$