Mohan bought a certain number of notebooks for ₹ 600. He sold $\dfrac{1}{4}$ of them at 5 percent loss. At what price should he sell the remaining notebooks so as to gain 10% on the whole ?

Given:

C.P. of notebooks = ₹ 600

Gain desired on the whole = 10 %

$\text{Profit\%} = \dfrac{\text{profit}}{\text{C.P}}\times 100$

Putting the values, we get

$10 = \dfrac{\text{Profit}}{600} \times 100\\[1em] \Rightarrow \text{Profit} = \dfrac{10 \times 600}{100}\\[1em] = \dfrac{6000}{100}\\[1em] = 60$

As we know,

$\text{Profit} = \text{S.P. - C.P.}$

Putting the values, we get

$60 = \text{S.P.} - 600\\[1em] \Rightarrow \text{S.P.} = 60 + 600\\[1em] = 660$

C.P. of $\dfrac{1}{4}$number of notebooks = ₹ $\dfrac{1}{4} \times 600$

= ₹ $\dfrac{600}{4}$

= ₹ $150$

Loss of $\dfrac{1}{4}$number of notebooks = 5%

$\text{Loss\%} = \dfrac{\text{Loss}}{\text{C.P}}\times 100$

Putting the values, we get

$5 = \dfrac{\text{Loss}}{150} \times 100\\[1em] \Rightarrow \text{Loss} = \dfrac{5 \times 150}{100}\\[1em] = \dfrac{750}{100}\\[1em] = 7.5$

As we know,

$\text{Loss} = \text{C.P. - S.P.}$

Putting the values, we get

$7.5 = 150 - \text{S.P.}\\[1em] \Rightarrow \text{S.P.} = 150 - 7.5\\[1em] = 142.5$

The S.P. of rest of notebooks = ₹ 660 - ₹ 142.5 = ₹ 517.5

The selling price of the rest of the notebooks = ₹ 517.50.