Question

if the price of petrol increased by Rs 2/liter,a person will have to buy i liter less petrol for Rs 1740. Find the original price at that time

Answer 1

$\boxed{\bold{\large{Answer:}}}$

$\text{Let\:the\:original\:price\:of\:petrol\:be\:x}$

$\text{Litres\:of\:petrol\:he\:purchasrd\:=\:1740/x}$

$\text{Increase\:in\:rate\:=\:x+2}$

$\text{Total\:no\:of\:litres\:=\:1740/x+2}$

$\text{According\:to\:the\:question,}$

$\implies \frac{1740}{x} - \frac{1740}{x + 2} = 1 \\ \\ \implies 1740(x + 2) - \frac{1740(x)}{(x)(x + 2)} = 1 \\ \\ \implies1740x + 3480 - \frac{1740x}{ {x}^{2} + 2x } = 1 \\ \\ \implies3480 = {x}^{2} + 2x \\ \\ \implies {x}^{2} + 2x - 3480 = 0 \\ \\ \implies {x}^{2} + 60x - 58x - 3480 = 0 \\ \\ \implies \: x(x + 60) - 58(x + 60) \\ \\ \implies(x + 60)(x - 58) \\ \\ \implies \: x = 58 \: and \: - 60$

$\text{We\:know\:that\:the\:price\:can't\:be\:negative,}$

$\text{Thus,\:the\:price\:for\:1\:litre\:of\:petrol\:is\:58Rs}$

$\boxed{\bold{\large{Hope\:it\:helps\:you!}}}$

Answer 2

$<b>Heya mate. (^_-). Solution below.$
====================================

• Let the original rate of petrol be 'x' Rs/L

• Total cost of petrol bought by person = 1740 Rs.

• Then, number of litres of petrol bought by person -

= total cost/rate

= 1740/x



• Now, if the price is increased by 2,

• New rate = x + 2 Rs/L

• Cost of petrol bought by person = 1740

• Then, number of litres of petrol bought -

= cost / rate

= 1740 / x + 2



• Now, if the price increases by 2 Rs, he will buy 1 L less petrol.

or, number of litres of petrol bought before increase in price - number of litres of petrol bought after increase in price = 1

=> [1740/x] - [1740/x + 2] = 1


=> [ {1740 × (x + 2)} - {1740 × (x)} ]/ (x)(x + 2) = 1


=> [ {1740x + 3480 } - {1740x} ]/x² + 2x = 1


=> 1740x - 1740x + 3480 = 1 × x² + 2x .. [multiplying x² + 2 with 1 on RHS)


=> 3480 = x² + 2x ....[cancelling 1740x and - 1740x on LHS]


=> 0 = x² + 2x - 3480 ...[shifting 3480 on RHS]


=> 0 = x² + 60x - 58x - 3480... [midterm split method]


=> 0 = x (x + 60) - 58 (x + 60)


=> 0 = (x - 58)(x + 60)



• By zero product rule,

x = 58

or, x = - 60


• Since, price can never be in negative, we take x as 58.


$<marquee> So, earlier price of petrol = 58 Rs/L.</marquee>$
====================================

$<u>Verification - </u>$


• Earlier, price of petrol was 58 Rs./L

=> So, total litre of petrol bought by person -

= 1740/58

= 30 L.



• If price is increased by 2 Rs/L, price becomes 60 Rs/L.

=> So, total litres of petrol bought by person

= 1740/60

= 29.



• Now, total litres of petrol bought before increase - total litres of petrol bought after increase = 1

=> 30 - 29 = 1

=> 1 = 1.

Hence, verified.
====================================

Thank you.. ;-)