The cost of 2 pens and 5 pencils is ₹ 57. If the cost of a pen is increased by ₹ 1.50 and that of a pencil is decreased by ₹ 1, then the cost of 5 pens and 3 pencils is ₹ 109. What is the original cost of 3 pens and 4 pencils ?

Calculation:

Let the original cost of one pen be 'p' rupees.

Let the original cost of one pencil be 'c' rupees.

2p + 5c = 57 (Equation 1)

New cost of a pen = (p + 1.50) rupees

New cost of a pencil = (c - 1) rupees

So, 5(p + 1.50) + 3(c - 1) = 109

5p + 7.50 + 3c - 3 = 109

5p + 3c = 104.50 (Equation 2)

Multiply Equation 1 by 3: (2p + 5c = 57) × 3 ⇒ 6p + 15c = 171 (Equation 3)

Multiply Equation 2 by 5: (5p + 3c = 104.50) × 5 ⇒ 25p + 15c = 522.50 (Equation 4)

Subtract Equation 3 from Equation 4:

(25p + 15c) - (6p + 15c) = 522.50 - 171

19p = 351.50

p = 351.50 / 19

p = 18.50

Now substitute the value of p = 18.50 into Equation 1 to find c:

2(18.50) + 5c = 57

37 + 5c = 57

5c = 57 - 37

c = 4

The original cost of 3 pens and 4 pencils:

Cost = 3p + 4c = 3(18.50) + 4(4) = 55.50 + 16

Cost = 71.50

∴ The original cost of 3 pens and 4 pencils is ₹ 71.50.