Question

Sachin and Anurag have monthly incomes in the ratio 6 : 7 and Their monthly expenditures in the ratio 5 : 4. If they save Rs. 700 and Rs. 2100 respectively, find the monthly expenditure of Anurag.​

Answer 1

Given :-

• Sachin and Anurag have monthly incomes in the ratio 6:7 and their monthly expenditures in the ratio 5:4.
• They save Rs 700 and Rs. 2100 respectively.

To find :-

• The Monthly expenditure of Anurag.

Solution :-

Let Monthly income of Sachin = Rs. 6x

Let Monthly income of Anurag = Rs. 7x

And,

Monthly expenditure of Sachin = Rs. 5y

Monthly expenditure of Anurag = Rs. 4y

Also given that,

• They save Rs. 700 and Rs. 2100 respectively.

★ According to Sachin,

$\tt{Monthly\: income-Monthly\: expenditure=700}$

$\implies\tt{6x-5y=700 - - - - (1)}$

★ According to Anurag,

$\tt{Monthly\: income-Monthly\: expenditure=2100}$

$\implies\tt{7x-4y=2100 - - - - (2)}$

Then, multiply 4 with equation (1) and 5 with equation (2),

• 24x-20y = 2800 ............ (1)
• 35x- 20y = 10500 .......... (2)

Now put equation (1) from equation (2),

$\implies\tt 35x - 20y -24x +20y = 10500-2800$

$\implies \tt 11x = 7700$

$\implies \tt x = 700$

Now put the value of x in equation (1),

$\tt 6x - 5y = 700$

$\implies \tt 6× 700 - 5y = 700$

$\implies \tt 4200 - 5y = 700$

$\implies \tt - 5y = - 3500$

$\implies \tt y = 700$

Answer :-

★ Monthly expenditure of Anurag = 4×700 = Rs. 2800

Answer 2

Answer:

Monthly expenditure of Anurag is Rs. 2800.

Step-by-step explanation:

Given :-

• Sachin and Anurag have monthly incomes in the ratio 6:7 and their monthly expenditures in the ratio 5:4.
• They save Rs 700 and Rs. 2100 respectively.

To find :-

• Monthly expenditure of Anurag.

Solution :-

Consider,

• Monthly income of Sachin = Rs. 6x
• Monthly income of Anurag = Rs. 7x

And,

• Monthly expenditure of Sachin = Rs. 5y
• Monthly expenditure of Anurag = Rs. 4y

They save Rs. 700 and Rs. 2100 respectively.

★According to Sachin,

$\sf{Monthly\: income-Monthly\: expenditure=700}$

$\to\sf{6x-5y=700...............(i)}$

★According to Anurag,

$\sf{Monthly\: income-Monthly\: expenditure=2100}$

$\to\sf{7x-4y=2100................(ii)}$

Now multiply 4 with eq(i) and 5 with eq(ii).

• 24x-20y = 2800............(i)
• 35x- 20y = 10500..........(ii)

Now subtract eq (i) from eq(ii).

35x - 20y -24x +20y = 10500-2800

→ 11x = 7700

→ x = 700

Now put x = 700 in equation (i).

6x - 5y = 700

→ 6× 700 - 5y = 700

→ 4200 - 5y = 700

→ - 5y = - 3500

→ y = 700

Therefore,

★ Monthly expenditure of Anurag = 4×700 = Rs. 2800