A person buys a few pens and a few pencils from a stationery shop for a total cost of ₹ 85. A pencil costs ₹ 5 and a pen costs ₹ 10. If the number of pencils bought is more than the number of pens bought, but less than twice the number of pens, then what is the number of pens bought ?

Let the number of pens be x and the number of pencils be y. Based on the given costs, the total expenditure equation is:

10x + 5y = 85

Dividing the entire equation by 5, we get: 2x + y = 17, which can be rewritten as y = 17 - 2x.

The problem provides two specific conditions:

• y > x (Number of pencils is more than pens): Substituting the value of y, we get 17 - 2x > x → 17 > 3x → x < 5.66.
• y < 2x (Number of pencils is less than twice the pens): Substituting the value of y, we get 17 - 2x < 2x → 17 < 4x → x > 4.25.

The only integer value for x that satisfies the range 4.25 < x < 5.66 is 5. Therefore, the number of pens bought is 5 (Option B).