Question

What is the cost of each pen?
I. Cost of 3 pens and 4 pencils is Rs. 10
II. Cost of 12 pencils and 9 pens is Rs. 30

• A. If the statement I alone is sufficient to answer the question.
• B. If the statement II alone is sufficient to answer the question.
• C. If the statements I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. If the statements I and II together are not sufficient to answer the question and additional data is required.

Hint:

When solving word problems involving the cost of items, form equations based on the given conditions and solve the system of equations to find the unknown values.

Answer 1

The Correct Option is D

Let the cost of a pen be \( p \) and the cost of a pencil be \( q \). From the first piece of information, we have the equation: \[ 3p + 4q = 10 \] From the second piece of information, we have the equation: \[ 12q + 9p = 30 \] Now, solve this system of equations. First, multiply the first equation by 3 and the second equation by 1 to make the coefficients of \( p \) the same: \[ 9p + 12q = 30 \] Subtract the first equation from the second: \[ (9p + 12q) - (3p + 4q) = 30 - 10 \] \[ 6p + 8q - 4q = 20 \] \[ 6p + 4q = 20 \] Now, divide through by 2: \[ 3p + 2q = 10 \] Next, subtract this equation from the first one: \[ (3p + 4q) - (3p + 2q) = 10 - 10 \] \[ 2q = 0 \] \[ q = 0 \] Now substitute \( q = 0 \) into the first equation: \[ 3p + 4(0) = 10 \] \[ 3p = 10 \] \[ p = \frac{10}{3} \approx 3.33 \] Thus, the cost of each pen is approximately Rs. 3.33. Since the answer closest to this is option 4, the correct answer is \( \boxed{4} \).