Question

A part of monthly expenses of a family is constant and the remaining varies with the

price of rice. When the cost of rice is Rs.250 per quintal, the monthly expenditure of the

family is Rs.1000 and when the cost of rice is Rs.240 per quintal the monthly expenditure is

Rs.980. Find the monthly expenditure of the family when the cost of rice is Rs.300 per

quintal.

Answer 1

Hi Nidra
Let the amount of wheat consumption of the family be x quintals and let the constant expenditure be y rupees.

So, formulating simultaneous equations based on the data given in the question:
250x + y = 1000 ---i)
240x + y = 980 ---ii)

Subtracting ii) from i), we get,
10x = 20
=> x = 2.
Putting x = 2 in equation i), we have
500 + y = 1000
=> y = 500.

Now, when the cost of wheat is Rs. 350,
we have the monthly expense as:
350 * 2 + 500 = 1200.

Thus, the montly expenditure is Rs. 1200.

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Answer 2

★ PROFIT AND LOSS ★

 

Let the constant expenditure be ₹x 

 

And, Let the consumption of rice by the family be y quintals. 

 

 

Now, $x + 250y = 1000$

And, $x+240y=980$

 

Subtracting (2) from (1) :

 

 

We get, $x + 250y =1000$

 

      −     $x + 240y = 980$

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

 

      So, $10y = 20$

 

 

Now, $y= 20/10$

 

∴ $y= 2$

Putting the value in (1),

 

We get, $x+250y=1000$

 

 

⇒ [tex]x + 250(2) = 1000[/tex]

 

 

⇒ $x+ 500 = 1000$

 

 

⇒ $x= 1000-500$

 

 

∴ $x=500$

 

 

 

Now, Total monthly expenditure when the cost of rice ₹300 = constant expenditure +  consumption of rice at ₹ 300 per quintal.

 

 

            $= x+300y$ 

 

            $= 500 + 300 * 2$

 

            $= 500+ 700$  →  From (3) and (4)

 

            $= Rs.1200$

 

 

Hence, the Total  monthly expenditure when the cost of rice ₹300 is ₹ 1200.