Example 7 A shopkeeper earns a profit of Rs 1 by selling one pen and incurs a loss of 40 paise per pencil while selling pencils of her old stock. (i) In a particular month she incurs a loss of Rs 5. In this period, she sold 45 pens. How many pencils did she sell in this period?Here, we donate
Profit by +
Loss by −
Profit on 1 pen = + 1 rupees =
Loss on 1 pencil = − 40 paisa
Total loss = −5 rupees
= −5 × 100 paisa
= −500 paisa
Number of pens sold = 45
Profit on pens sold = 45 × 100 paisa
= 4500 paisa
Also,
Loss on pencils sold = (−40) × No. of pencils sold
Now,
Total loss = Profit on pens sold + Loss on pencil sold
−500 = 4500 + (−40) × Number of pencils sold
−500 − 4500 = (−40) × Number of pencils sold
−(500 + 4500) = (−40) × Number of pencils sold
−(4500 + 500) = (−40) × Number of pencils sold
−5000 = (−40) × Number of pencils sold
(−5000)/(−40) = Number of pencils sold
500/4 = Number of pencils sold
125 = Number of pencils sold
Number of pencils sold = 125
∴ Number of pencils sold = 125
Example 7 A shopkeeper earns a profit of Rs 1 by selling one pen and incurs a loss of 40 paise per pencil while selling pencils of her old stock. (ii) In the next month she earns neither profit nor loss. If she sold 70 pens, how many pencils did she sell?Total profit/loss = 0
Number of pens sold= 70
Profit on pens sold = 70 × 100 paisa
= 7000 paisa
Also,
Loss on pencil sold = (−40) × No. of pencils sold
Now,
Total profit/loss = Profit on pens sold + Loss on pencil sold
0 = 7000 + (−40) × Number of pencils sold
0 − 7000 = (−40) × Number of pencils sold
−7000 = (−40) × Number of pencils sold
( − 7000)/(−40) = Number of pencils sold
700/4 = Number of pencils sold
175 = Number of pencils sold
Number of pencils sold = 175
∴ Number of pencils sold = 175

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.