# CBSE Class 10-Mathematics: Chapter – 3 Pair of Linear Equation in Two Variables Part 18 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 ₹ for a book kept for seven days, while Sury paid ₹ 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 ₹ .

According to question,

Or

And

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