Question

If the price of potatoes is reduced by $25\%$, one can buy $6.25$ kg more for Rs. $100$. The reduced price of potatoes is

• A. Rs. $3$/- per kg
• B. Rs. $3.50$ per kg
• C. Rs. $4$/- per kg
• D. Rs. $4.50$ per kg

Answer 1

Answer: (C)

Rs. $4$/- per kg

Let original price per kg $=x$.

Reduction $=25$%

$\therefore$ New price per kg $=x(1-\frac{25}{100})$

$=\frac{3x}{4}$

Now, for $Rs100$, let customer buy ${}^{\prime }{y}^{\prime }$ kg of potatoes.

$\therefore 100=$ (initial price per kg) $\times$ (weight bought)

$\Rightarrow 100=xy⟶\left(i\right)$

For the reduced cost,

$100=$ (new price per kg) $\times$ (weight bought)

$\Rightarrow 100=\left(\frac{3x}{4}\right)(y+6.25)$

But from eq $\left(i\right)$ $100=xy$

$\therefore xy=\frac{3x}{4}(y+6.25)$

$\Rightarrow 4y=3y+18.75$

$\Rightarrow y=18.75$

$\therefore x=\frac{100}{18.75}=\frac{100\times 100}{1875}$

$\therefore$ Reduced price $=\frac{3x}{4}=\frac{3}{4}\times \frac{100\times 100}{1875}$ per kg

$=4$ per kg