Narendra and Gopal Bhar friend they went to a stationary shop to purchase pen and pencil purchase 2pen and 3 pencil pencil for rupees 23. where as a Gopal purchase some kind of 3 pen and 5 pencil for rupees 36 find the cost of a pen and pencil
Answers
Let the cost of a pen is Rs. x and the cost of a pencil is Rs. y.
Narendra and Gopal Bhar were two friends.
Narendra went to a stationery shop to purchase pen and pencil purchase 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 Bhar 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
Step-by-step explanation:
Given -
- Narendra purcahased 2 pen and 3 pencils for Rs. 23
- Gopal purcahased same kind of 3 pen and 5 pencils for Rs. 36
To Find -
Cost of a pen and pencil.
Let x be the cost of pen and y be the cost of pencils.
Then,
2x + 3y = 23
and
3x + 5y = 36
Now,
Solving this equations -
2x + 3y = 23
3x + 5y = 36
By Elimination method,
{2x + 3y = 23} × 3
{3x + 5y = 36} × 2
= 6x + 9y = 69
6x + 10y = 72
(-) (-) (-)
--------------------------
- y = - 3
- = y = 3
Now,
Substituting the value of y on
3x + 5y = 36
= 3x + 5(3) = 36
= 3x + 15 = 36
= 3x = 36 - 15
= 3x = 21
= x = 21/3
- = x = 7
Hence,
The cost of pen is 7
and
The cost of pencil is 3
Verification -
Substituting the value of x and y on 2x + 3y = 23
= 2(7) + 3(3) = 23
= 14 + 9 = 23
= 23 = 23
LHS = RHS
Now,
Substituting the value of x and y on 3x + 5y = 36
= 3(7) + 5(3) = 36
= 21 + 15 = 36
= 36 = 36
LHS = RHS
Hence,
Verified..