Question

the age of Ramesh and Suresh is 4:7 five years from now of their will be 3:5 find their present age? ​

Answer 1

Step-by-step explanation:

$\frak Given = \begin{cases} &\sf{The\ ratio\ of\ the\ age\ of\ Ramesh\ and\ Suresh\ is\ 4\ :\ 7.} \\ &\sf{After\ five\ years,\ the\ ratio\ of\ their\ age\ will\ be\ 3\ :\ 5.} \end{cases}$

To find:- We have to find their present ages ?

☯️ Let the present ages of Ramesh and Suresh be 4x and 7x.

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$\frak{\underline{\underline{\dag We\ know\ that,\ after\ five\ years\ their\ ages\ will\ be:-}}}$

$\sf : \implies {Age\ of\ Ramesh\ =\ \bf 4x\ +\ 5.}$

$\sf : \implies {Age\ of\ Suresh\ =\ \bf 7x\ +\ 5.}$

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$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\bf : \implies {(4x\ +\ 5)\ :\ (7x\ +\ 5)\ =\ 3\ :\ 4} \\ \\ \bf : \implies {\dfrac{4x\ +\ 5}{7x\ +\ 5}\ =\ \dfrac{3}{5}} \\ \\ \sf : \implies {\pink{\boxed{\bf [By\ cross\ multiplication,\ we\ get:-]}}} \\ \\ \bf : \implies {4\ \times\ (4x\ +\ 5)\ =\ 3\ \times\ (7x\ +\ 5)} \\ \\ \bf : \implies {16x\ +\ 20\ =\ 21x\ +\ 15} \\ \\ \bf : \implies {21x\ -\ 16x\ =\ 20\ -\ 15} \\ \\ \bf : \implies {5x\ =\ 5} \\ \\ \bf : \implies {x\ =\ \cancel \dfrac{5}{5}\ =\ 1} \\ \\ \bf : \implies {\purple{\underline{\boxed{\bf x\ =\ 1.}}}}\bigstar$

So here:-

$\sf : \implies {Age\ of\ Ramesh\ =\ 4x\ =\ 4\ \times\ 1\ =\ \bf 4\ years.}$

$\sf : \implies {Age\ of\ Suresh\ =\ 7x\ =\ 7\ \times\ 1\ =\ \bf 7\ years.}$

Hence verified ✔.

Answer 2

Let the ages of Ramesh, Suresh and Mahesh be represented by R, S, M respectively.

Now, given M=R+45

(R+5)/(S+5) = 2/5

=> 5R + 25= 3S +1 0

=> 3S - 5R = 15 --------------(1)

Also,

(M-15)/(S-15) = 3/2

Putting M= R+45,

=> (R+30)/(S-15)= 3/2

=> 2R + 60= 3S - 45

=> 3S-2R = 105 ------------------(2)

Subtracting (1) from (2),

3S - 2R = 105

-(3S - 5R = 15)

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

3R = 90

=> R= 30.

Therefore,

M=R+45

M= 30 + 45= 75.

3S - 2R = 105

=> 3S - 60= 105

=> 3S = 45

=> S = 15.

Therefore, average of present ages

=(75+15+30)/3

=40. _______________Ans

Hope it's helpful :)(