25. Narendra and Gopal were friends. They went to a stationary shop to purchase pen and penals
Narendra purchase 2 pen and 3 pencil for Rs. 23, where as Gopal purchase same kind of 3 pen and 5
pencil for Rs. 36. Find the cost of a pen and a pencil.
Answers
Step-by-step explanation:
Let the cost of a pen is Rs. x and the cost of a pencil is Rs. y.
Narendra and Gopal were two friends.
Narendra went to a stationery shop to purchase pen and pencil and purchased 2 pens and 3 pencils for Rs. 23.
So, Total Rupees = x × (number of pens) + y × (number of pencils)
→ 23 = x(2) + y(3)
→ 23 = 2x + 3y............... (1)
Similarly, Gopal purchases some kind of 3 pens and 5 pencils for Rs 36.
→ 36 = x(3) + y(5)
→ 36 = 3x + 5y............... (2)
On multiplying (eq 1) by 3 and (eq 2) by 2.
We get,
→ 69 = 6x + 9y
→ 72 = 6x + 10y
On comparing them, we get,
→ 69 - 9y = 72 - 10y
→ 69 - 72 = - 10y + 9y
→ -3 = - y
→ y = 3
Substitute value of y = 3 in eq (1)
→ 23 = 2x + 3(3)
→ 23 = 2x + 9
→ 2x = 23 - 9
→ 2x = 14
→ x = 7
Therefore, Cost of a pen is Rs. 7 and a pencil is Rs. 3.