Question

Raveena is 7 years older than her sister Praveena. The sum of their ages six years later will be 35. Find their present ages.
A. Raveena = 8 years, Praveena 15 years
B. Raveena = 14 years, Praveena = 9 years
C. Raveena 15 years, Praveena = 8 years
D. None of these

Answer 1

Hint:-We will consider Praveena’s age to be ‘x’. As we know that the present age of Raveena is 7 years older than Praveena. Therefore, the age of Raveena would be (x + 7).After 6 years, age of praveena will be x+6 and raveena will be x+7+6 i.e. x+13 and they given condition that sum of ages of both after six years will be 35 So,we can write x+6+x+13=35 .Hence solve the linear equation and calculate value for x.

Complete step-by-step answer:
As mentioned in the hint, Praveena’s age is ‘x’ and the age of Raveena is (x + 7).
Present age of Praveena = x
Present age of Raveena = (x + 7)
So, age of Praveena after 6 years = (x + 6)
And, age of Raveena after 6 years = (x + 7 + 6) = (x + 13)
As mentioned in the question, the sum of the ages of Raveena and Praveena after 6 years will be 35.
Therefore, (x + 13) + (x + 6) = 35
2x + 19 = 35
2x = 35 – 19
x = \[\dfrac{16}{2}\] = 8
So, as the value of ‘x’ is 8, therefore, Praveena’s age is 8 and the age of Raveena is (x + 7) = (8 + 7) = 15
Age of Praveena = 8
Age of Raveena = (8 + 7) = 15
Hence, the answer of the question is (c) Raveena = 15 years, Praveena = 8 years.

Note:-Students should know forming of an equation i.e converting statements into mathematical form by using conditions given in the question and we have to choose a variable depending upon the statement or condition given and Hence calculate for assumed variable.If there are two variables involved then we get two equations ,by solving these two equations we get value of variables.