RD Chapter 3 Pair of Linear Equations in Two Variables Ex 3.9 Solutions
Question - 11 : - The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju as tiwce as old as his sister Cathy. The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju.
Answer - 11 : -
Let age of Ani = x years
and age of Biju = y years
x – y = 3 ….(i)
Ani’s father Dharam’s age = 2x
and Cathy’s age = (1/2) y
But 2x – (1/2) y = 30
=> 4x – y = 60 ….(ii)
Subtracting,
3x = 57
x = 19
and 4x – y = 60
=> 4 x 19 – y = 60
=> 76 – y = 60
=> 76 – 60 = y
=> y = 16
Anil’s age = 19 years
and Biju’s age = 16 years
Question - 12 : - Two years ago, Salim was thrice as old as his daughter and six years later, he will be four years older than twice her age. How old are they now? [NCERT Exemplar]
Answer - 12 : -
Let Salim and his daughter’s age be x and y year respectively.
Now, by first condition,
Two years ago, Salim was thrice as old as his daughter.
i. e., x – 2 = 3(y – 2)
=> x – 2 = 3y – 6
=> x – 3y = -4 …(i)
and by second condition,
six years later, Salim will be four years older than twice her age.
x + 6 = 2(y + 6) + 4
=> x + 6 = 2y + 12 + 4
=> x – 2y = 16 – 6
=>x – 2y = 10 …(ii)
On subtracting Eq. (i) from Eq. (ii), we get
y = 14
Put the value of y in Eq. (ii), we get
x – 2 x 14 = 10
=> x = 10 + 28
=> x = 38
Hence, Salim and his daughter’s age are 38 years and 14 years, respectively.
Question - 13 : - The age of the father is twice the sum of the ages of his two children. After 20 years, his age will be equal to the sum of the ages of his children. Find the age of the father. [NCERT Exemplar]
Answer - 13 : -
Let the present age (in year) of father and his two children be x, y and z year, respectively.
Now by given condition, x = 2(y + z) …(i)
and after 20 years,
(x + 20) = (y + 20) + (z + 20)
=> y + z + 40 = x + 20
=> y + z = x – 20
On putting the value of (y + z) in Eq. (i) and we get the present age of father
=> x = 2 (x – 20)
x = 2x – 40
=> x = 40
Hence, the father’s age is 40 years.