# Question:1

If Ritu were younger by 5 years than what she really is, then the square of her age would have been 11 more than five times her present age. What is her present age ?                   [CBSE Term-2 SQP 2022]

## Solution:

Let, the present age of Ritu be ‘x’ years.

Then, according to the question

(x – 5)² = 5x + 11

⇒   x² – 10 x + 25 = 5x + 11

⇒   x² – 15x + 14 = 0

⇒  x² – 14x – x + 14 = 0

⇒  x(x – 14) – 1(x – 14) = 0

⇒   (x – 14)(x – 1) = 0

⇒   x = 1, 14

But x = 1 is not possible, as in this case, (x – 5) will be negative.

∴   x  = 14

hence, the present age of Ritu is 14 years.

# Question 2:

The sum of areas of two squares is 157 m². If the sum of their perimeters is 68 m, find the sides of the two squares.                     [CBSE 2019]

# Question 3:

If the equation (1 + m²)x² + 2 mcx + c² – a² = 0 has equal roots then show that c² = a²(1 + m²).

[CBSE 2017]

# Question 4:

A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, it would have taken 3 hours more to cover the same distance. Find the original speed of the train.                [CBSE    2020]

# Question 5:

In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200km/hr and time of flight increased by 30 minutes. Find the original duration of flight .      [CBSE  2020]

# Question 6:

A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hours less for the same journey. Find the speed of the train.                                                                                   [CBSE  2019] 