The cost of 3 pens and 5 pencils is Rs. 74. The cost of 5 pens and 7 pencils exceeds the cost of 4 pens and 3 pencils by Rs. 34, What is the cost of 2 pens and 9 pencils?  

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  1. Rs. 50
  2. Rs. 65
  3. Rs. 70
  4. Rs. 72

Answer (Detailed Solution Below)

Option 4 : Rs. 72
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Detailed Solution

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Given:

The cost of 3 pens and 5 pencils is ₹74.

The cost of 5 pens and 7 pencils exceeds the cost of 4 pens and 3 pencils by ₹34.

Calculations: 

Let the cost of one pen be ₹x and the cost of one pencil be ₹y.

3x + 5y = 74       ....(i)

Cost of 5 pens and 7 pencils exceeds the cost of 4 pens and 3 pencils by ₹34.

5x + 7y = 4x + 3y + 34

⇒ x + 4y = 34       ....(ii)

Now, solve equations (i) and (ii):

From (ii): x = 34 - 4y

Substitute x in (i):

3(34 - 4y) + 5y = 74

⇒ 102 - 12y + 5y = 74

⇒ 7y = 28 ⇒ y = 4

Substitute y in (ii):

x + 4(4) = 34 ⇒ x = 18

Now, we need the cost of 2 pens and 9 pencils:

2x + 9y = 2(18) + 9(4)

⇒ 2x + 9y = 36 + 36 = 72

∴ The correct answer is option (4).

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