A shopkeeper buys pens and pencils at ₹ 5 and ₹ 1 per price respectively. For every two pens, he buys three pencils. He sold pens and pencils at 12% and 10% profit respectively. If his total sale is ₹ 725, then find the number of pens and pencils sold by him.

Let x be the number of pens sold and y be the number of pencils sold.

Given,

Cost Price (CP) of 1 pen = ₹ 5

Profit on pens = 12%

⇒ SP of 1 pen = CP of pen + (Profit % of CP)

⇒ SP of 1 pen = 5 + $\dfrac{12}{100} \times 5$ = 5 + 0.12 × 5 = 5 + 0.60 = ₹ 5.60

Given,

Cost Price (CP) of 1 pencil = ₹ 1

Profit on pencils = 10%

SP of 1 pencil = CP of pencil + (Profit % of CP)

SP of 1 pencil = 1 + $\dfrac{10}{100}$ × 1 = 1 + 0.10 = ₹ 1.10

For every two pens, he buys three pencils,

This means the ratio of pens to pencils is x : y = 2 : 3.

$\dfrac{x}{y} = \dfrac{2}{3}$

⇒ y = $\dfrac{3}{2}x$     …….(1)

Given,

Total sale is ₹ 725,

⇒ x × 5.60 + y × 1.10 = 725

⇒ 5.60x + 1.10y = 725     ……(2)

Substitute the expression for y from equation (1) in (2), we get :

⇒ 5.60x + 1.10 $\times \dfrac{3}{2}x$ = 725

⇒ 5.60x + 1.10 × 1.5 = 725

⇒ 5.60x + 1.65x = 725

⇒ 7.25x = 725

⇒ y = $\dfrac{725}{7.25}$ = 100.

Substituting value of y in equation 1 we get,

⇒ y = $\dfrac{3}{2} \times 100$

⇒ y = 3 × 50

⇒ y = 150.

Hence, the number of pens sold = 100 and number of pencils sold = 150.