The cost of 2 pencils and 3 pens is ₹55 and the cost of 7 pencils and 2 pens is ₹65. What is the total price (in ₹) of one pen and one pencil?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 20.
Let the cost of one pencil = x
the cost of one pen = y.
The cost of 2 pencils and 3 pens is ₹55 = 2x + 3y = 55 -----------(1)
The cost of 7 pencils and 2 pens is ₹65 = 7x + 2y = 65 ------------(2)
Multiply the first equation by 2 to align the number of pens:
⇒ 4x + 6y = 110
Multiply the second equation by 3:
⇒ 21x + 6y = 195
Now subtract the first equation from the second:
⇒ (21x + 6y) − (4x + 6y) = 195 − 110
⇒ 17x = 85
⇒ x = 5
Put the value of x in the equation first:
⇒ 2(5) + 3y = 55
⇒ 10 + 3y = 55
⇒ 3y = 55 − 10 = 45
⇒ y = 45/3 = 15
The total price of one pencil and one pen is = x + y = 5 + 15 = 20