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 ?Â  Â  Â  Â  Â  Â  Â  Â  Â  Â [CBSE Term-2 SQP 2022]

Solution:

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

Then, according to the question

(x – 5)Â² = 5x + 11

â‡’Â  Â xÂ² – 10 x + 25 = 5x + 11

â‡’Â  Â xÂ² – 15x + 14 = 0

â‡’Â  xÂ² – 14x – x + 14 = 0

â‡’Â  x(x – 14) – 1(x – 14) = 0

â‡’Â  Â (x – 14)(x – 1) = 0

â‡’Â  Â x = 1, 14

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

âˆ´Â  Â xÂ  = 14

hence, the present age of Ritu is 14 years.

Question 2:

The sum of areas of two squares is 157 mÂ². If the sum of their perimeters is 68 m, find the sides of the two squares.Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â [CBSE 2019]

Question 3:

If the equation (1 + mÂ²)xÂ² + 2 mcx + cÂ² – aÂ² = 0 has equal roots then show that cÂ² = aÂ²(1 + mÂ²).

[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.Â  Â  Â  Â  Â  Â  Â  Â  [CBSEÂ  Â  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 .Â  Â  Â  [CBSEÂ  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.Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â [CBSEÂ  2019]