Question

If price of sugar decrease by Rs. 5, one can buy 1 kg more sugar in Rs. 150, what is the
price of the Sugar​

Answer 1

The price of sugar is Rs. 30

Step-by-step explanation:

Let the cost of 1 kg sugar be Rs. x .

In Rs. 150, 150/x kg sugar can be bought.

When the price of sugar is decreased by Rs. 5, its cost price be Rs. (x - 5)

In Rs. 150, 150/(x - 5) kg sugar can be bought.

According to the question,

150/(x - 5) = 150/x + 1 [ where x ≠ 0, 5 ]

or, 150/(x - 5) = (150 + x)/x

or, 150x = (x - 5) (150 + x)

or, 150x = 150x + x² - 750 - 5x

or, x² - 5x - 750 = 0

or, x² - 30x + 25x - 750 = 0

or, x (x - 30) + 25 (x - 30) = 0

or, (x - 30) (x + 25) = 0

Since x > 0, then x = 30

Therefore the price of sugar is Rs. 30

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

Price of sugar

= Rs. p

Hence,

${\boxed{\sf\:{Sugar\;in\;Rs.150}}}$

$\tt{\rightarrow\dfrac{150}{p}}$

Price is decrease by Rs.5/kg

Price = (p - 5)

Then,

Sugar in Rs.150

$\tt{\rightarrow\dfrac{150}{p-5}}$

Bought 1 kg more

Situation

$\tt{\rightarrow\dfrac{150}{p-5}-\dfrac{150}{p}=1}$

$\tt{\rightarrow\dfrac{150p-150(p-5)}{(p-5)\times p}}$

150p - 150p + 750 = p² - 5p

p² - 5p - 750 = 0

Hence,

p² - 5p - 750 = 0

p² - 30p + 25p - 750 = 0

p(p - 30) + 25(p - 30) = 0

(p - 30)(p + 25) = 0

Therefore,

Negative value is not applicable

Hence,

p = 30

$\Large{\boxed{\sf\:{Price\;of\;sugar = Rs.30/kg.}}}$