present age of mother of Manish is 1 year more than 5 times the present age of Manish. four years before if the product of their ages was 22 then find the present age of Manish and his mother
Answers
Answer:
present age of Manish is 5 yrs and his mother is 26 yrs
Step-by-step explanation:
Let the present age of Manish be x yrs and his mother be (5x+1).
From the given condition,
(x-4)(5x+1-4)=22
(x-4)(5x-3)=22
x(5x-3)-4(5x-3)=22
5x²-3x-20x+12=22
5x²-23x+12-22=0
5x²-23x-10=0
5x²-25x+2x-10=0
5x(x-5)+2(x-5)=0
(x-5) (5x+2)=0
x-5=0 or 5x+2=0
x=5 or x=-2/5
age is not negetive
therefore x=5
age of Manish =5yrs
age of Manish's mother=26yrs
Given :- Present age of mother of Manish is 1 year more than 5 times the present age of Manish. four years before if the product of their ages was 22 then find the present age of Manish and his mother ?
Solution :-
Let us assume that, present age of manish is x years.
case 1) :-
→ Manish mother's age = 5 * manish age + 1 .
→ Manish mother's age = (5x + 1) years .
case 2) :-
→ Four years before manish was = (x - 4) years old .
→ Four years before manish's mother was = (5x + 1) - 4 = (5x - 3) years old .
A/q,
→ (x - 4){(5x + 1) - 4} = 22
→ (x - 4)(5x - 3) = 22
→ 5x² - 3x - 20x + 12 = 22
→ 5x² - 23x + 12 - 22 = 0
→ 5x² - 23x - 10 = 0
→ 5x² - 25x + 2x - 10 = 0
→ 5x(x - 5) + 2(x - 5) = 0
→ (x - 5)(5x + 2) = 0
→ x = 5 or (-2/5) .
therefore,
→ Present age of Manish = 5 years. (Ans.)
→ Present age of Manish's mother = (5x + 1) = (5*5 + 1) = 26 years. (Ans.)
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