# CBSE Class 10-Mathematics: Chapter –3 Pair of Linear Equation in Two Variables Part 18

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**Question 12:**

The sum of a two-digit number and the number obtained by reversing the order of digits is 99. If the digits differ by 3, find the number.

**Answer:**

Let the digit at unit place be and tens place be .

According to question,

Or

And

Or

On solving eq. (i) and (ii), we get

Then the original number is

On solving eq. (i) and (iii), we get,

**Question 13:**

In a cyclic quadrilateral ABCD, and Find the four angles.

**Answer:**

In cyclic quadrilateral

And

On solving eq. (i) and (ii), we get,

**Question 14:**

A two-digit number is obtained by either multiplying the sum of the digits by 8 and adding 1 or by multiplying number. How many such numbers are there?

**Answer:**

Let digit at unit place and tens place then

Original number

According to question,

Or

Or

Or

On solving eq. (i) and (ii), we get,

Which is not possible

Or

On solving eq. (i) and (ii) we get,

Only one number exist.

**Question 15:**

A leading library has a fixed charge for the first three days and an additional charge for each day thereafter Sarika paid Rs. for a book kept for seven days, while Sury paid Rs. for the book she kept for five days, find the fixed charge and the charge for each extra day.

**Answer:**

Let the fixed charge be and additional charge be Rs .

According to question,

Or

And

On solving eq. (i) and (ii), we get