Renu sold an article at a loss of 8 percent. Had she bought it at 10% less and sold for ₹ 36 more, she would have gained 20%. Find the cost price of the article.

Let the C.P. of the article be ₹ $100$.

Loss% = 8%

As we know

$\text{Loss\% } = \dfrac{\text{Loss}}{\text{C.P.}} \times 100 \\[1em] \Rightarrow 8 = \dfrac{\text{Loss}}{100} \times 100 \\[1em] \Rightarrow 8 = \dfrac{\text{Loss}}{\cancel{100}} \times \cancel{100}\\[1em] \Rightarrow \text{Loss} = 8$

And

$\text{Loss = C.P. - S.P.}\\[1em] \Rightarrow 8 = 100 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 100 - 8\\[1em] \Rightarrow \text{S.P.} = 92$

When C.P. of the article is 10% less.

$= 100 - \dfrac{10}{100} \times 100\\[1em] = 100 - \dfrac{10}{\cancel{100}} \times \cancel{100}\\[1em] = 100 - 10\\[1em] = 90$

The gain % = 20%.

As we know

$\text{Gain\% } = \dfrac{\text{Gain}}{\text{C.P.}} \times 100 \\[1em] \Rightarrow 20 = \dfrac{\text{Gain}}{90} \times 100 \\[1em] \Rightarrow \text{Gain} = \dfrac{20 \times 90}{100}\\[1em] \Rightarrow \text{Gain} = \dfrac{1800}{100}\\[1em] \Rightarrow \text{Gain} = 18$

And

$\text{Gain = S.P. - C.P.}\\[1em] \Rightarrow 18 = \text{S.P.} - 90\\[1em] \Rightarrow \text{S.P.} = 18 + 90\\[1em] \Rightarrow \text{S.P.} = 108$

Difference in Selling Price = ₹ 108 - ₹ 92 = ₹ 16

Applying unitary method:

When sold for ₹ $16$ more, the C.P. of the article = ₹ $100$.

When sold for ₹ $36$ more, the C.P. of the article = ₹ $\dfrac{100}{16} \times 36 = ₹ 225$.

Hence, cost price of the article = ₹ $225$.