The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs.14/litre and 1220 litres of milk each week at Rs. 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs.17/litre?

Let selling price is denoted by = Rs. Y and demand = x litre.

A.T.Q. y = ax + b …(i)

Now, when x = 980 litre, and y = Rs.14/litre

14 = 980 a + b …(ii)

Again when x = 1220 and y = Rs.16/litre

16 = 1220 a + b …(iii)

From (ii) and (iii), we get

1220a – 980 a = 2

or 240a = 2

or a =

Putting the value of a in (ii)

980 × = 14

⇒ b = 14 -

= = =

Now a = and b = and y = 17

From y = ax + b

17 = × x +

× 17 -

-

x = = 1340

Hence, x = 1340 litres.

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