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]
Solution: For solution please click here
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]
Solution:For solution pleaseclick here
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]
Solution: For solution please click here
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]
Solution : For solution please click here
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]
Solution: For solution please click here