1) At present, the sum of ages of father and daughter is 65 years. What will be the sum of their ages after 7 years? (A) 72 (B) 79 (C) 86 (D) 75
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Let the ages of father and his son be x and y respectively.
Case I:- The sum of the ages of father and his son is 65 years.
age of father + age of son = 65
⇒x+y=65⟶(i)
Case II:- After 5 years, fathers age will be twice the age of his son.
Age of father = 2 (age of son)
⇒x+5=2(y+5)
⇒x+5=2y+10
⇒x=2y+5⟶(ii)
From eq
n
(i)&(ii), we have
(2y+5)+y=65
⇒3y=65−5
⇒y=20
Substituting the value of y in eq
n
(i), we have
x+20=65
⇒x=45
Hence, the present age of father and son is 45 and 20 respectively and equation (i)&(ii) are the pair of linear equations in two variables.
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