Question

7. Monthly incomes of two persons Ram and Rahim are in the ratio 5.7 and their monthly expende
are in the ratio 7:11. If each of them saves 60 per month. Find their monthly income.
(ICWA (F) 2003) (Ans. 200,3 280)


can some one me this in step​

Answer 1

AnswEr :

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

Monthly incomes of two persons Ram and Rahim are in the ratio 5:7 and their monthly expenditures are in the ratio 7:11. If each of them saves 60 per month.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

Their monthly income.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Let the monthly income of Ram = Rs.5r

Let the monthly income of Rahim = Rs.7r

&

The monthly expenditure of Ram = Rs.7m

The monthly expenditure of Rahim = Rs.11m

$\bf{\pink{\underline{\underline{\tt{A.T.Q\::}}}}}$

$\leadsto\sf{5r-7m=60..............(1)}\\\\\leadsto\sf{7r-11m=60............(2)}$

$\blacksquare\bf{\underline{\underline{\bf{Using\:substitution\:method\::}}}}}$

From equation (1),we get;

$\mapsto\tt{5r-7m=60}\\\\\mapsto\tt{5r=60+7m}\\\\\mapsto\tt{r=\dfrac{60+7m}{5} ................(3)}$

Putting the value of r in equation (2),we get;

$\mapsto\tt{7\bigg(\dfrac{60+7m}{5} \bigg)-11m=60}\\\\\\\mapsto\tt{\dfrac{420+49m}{5} -11m=60}\\\\\\\mapsto\tt{420+49m-55m=300}\\\\\\\mapsto\tt{420-6m=300}\\\\\\\mapsto\tt{-6m=300-420}\\\\\\\mapsto\tt{-6m=-120}\\\\\\\mapsto\tt{m=\cancel{\dfrac{-120}{-6} }}\\\\\\\mapsto\tt{\red{m=20}}$

Putting the value of m in equation (3), we get;

$\mapsto\tt{r=\dfrac{60+7(20)}{5} }\\\\\\\mapsto\tt{r=\dfrac{60+140}{5} }\\\\\\\mapsto\tt{r=\cancel{\dfrac{200}{5} }}\\\\\\\mapsto\tt{\red{r=40}}$

Therefore;

$\bf{\orange{\boxed{\bf{THEIR\:\:MONTHLY\:\:INCOMES\::}}}}}$

$\underbrace{\sf{The\:monthly\:Income\:of\:Ram=5r=(5\times 40)=Rs.200}}}}}\\\underbrace{\sf{The\:monthly\:Income\:of\:Rahim=7r=(7\times 40)=Rs.280}}}}}$

Answer 2

⭐Brainly Quality Answer ⭐

Answer :-

The monthly income of Ram is rs200 & Rahim is rs280.

Calculation :-

Given :-

Monthly incomes of two persons Ram and Rahim are in the ratio 5:7 and their monthly expenditures are in the ratio 7:11. If each of them saves 60 per month.

We have to find???

Their monthly income.

Solution :-

Let the monthly income of Ram = Rs.5r

Let the monthly income of Rahim = Rs.7r

&

The monthly expenditure of Ram = Rs.7×m

The monthly expenditure of Rahim = Rs.11×m

A.T.Q :-

5r-7m=60...........(1)

7r-11m=60...........(2)

Use Elimination Method :-

5r-7m=60...........(1) × 7

7r-11m=60...........(2) × 5

__________________

35r-49m= 420.......(3)

+35r-55m =300.......(4)

- + -

________________

6m = 120

=> m =20

_________________________________

Putting in 1 equation :-

5r-7m=60, where m=20

=>5r-7×20=60

=>5r=60+140

=>5r =200

$= > r \: = \frac{200}{5}$

=> r = 40

__________________

So, Value of r =40

The monthly income of Ram = Rs.5r

=> 5× 40

=> rs. 200

The monthly income of Rahim = Rs.7r

=> 7× 40

=> rs. 280

Hence, Solved✔✔✔

______________________________________

Regards,