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

Question :-- If price of sugar decrease by Rs. 5 per kg, one can buy 1 kg more sugar in Rs. 150, What is the price of the Sugar ?

Solution :---

→ Let price of sugar per kg = Rs.x

→ Than He bought sugar in Rs.150 = (150/x) kg .

Now, it is said that, price is decrease by Rs.5 per kg .

→ new price of sugar per kg now, = Rs.(x-5)

→ So, He bought sugar in Rs.150 = (150/x-5) kg

Now, it is said that , he bought 1 kg more ,

So,

→ (150/x-5) - (150/x) = 1

→ [ 150x - 150(x-5) ] / (x-5)*x

→ [ 150x - 150x + 750 ] = x² - 5x

→ x² - 5x - 750 = 0

Splitting the middle term now,

→ x² - 5x - 750 = 0

→ x² - 30x + 25x - 750 = 0

→ x(x-30) + 25(x-30) = 0

→ (x-30)(x+25) = 0

So,

→ x = 30 or (-25) { negative value not possible.}

Hence, Price of sugar is Rs.30/kg.

Answer 2

Answer:

${\boxed{\bold{Price\:of\:sugar=Rs.30}}}$

Step-by-step explanation:

Given that,

• Price of sugar decreased by = Rs.5
• One can buy 1 kg more in Rs.150
• Price of sugar = ?

Let the price of 1 kg sugar be Rs. M .

$\therefore$ Rs.150 can be used to buy = (150/M) kg.

If the price is decreased by Rs.5,

Then, he can buy (150/M-5) kg in Rs.150.

${\underline{\underline{\bold{According\:to\:question:-}}}}$

→ $\sf \dfrac{150}{M-5} - \dfrac{150}{M} = 1$

→ $\sf \dfrac{150M-150(M-5)}{M(M-5)} = 1$

→ $\sf \dfrac{\cancel{150M-150M}+750}{M(M-5)} = 1$

→ $\sf {M}^{2} - 5M = 750$

→ $\sf {M}^{2} - 5M - 750 = 0$

→ $\sf {M}^{2} - 30M + 25M - 750 = 0$

→ $\sf M(M-30) + 25(M - 30) = 0$

→ $\sf (M+25)(M-30) = 0$

→ $\sf (M+25) = 0 \: \: or, \: \: (M-30) = 0$

→ $\sf M = -25 \: \: or,\: \: M = 30$

$\therefore{\boxed{\sf {M = 30 \: \: [\because Price\: can't\: be\: negative]}}}$

${\underline{\therefore{\bold{Price\:of\:1\:kg\:sugar=Rs.30}}}}$