Question

6. Aman is 5 times as old as his son. He will be three times as old a his son after 10 yrs. Find their present ages.

7. The sum of three consecutive numbers is 306. Find the numbers.
ubtracted from three times a certain number the result is 6 more than twice the number. Find the number.​

Answer 1

$\huge \fbox \green{❤Solution:}$

$\sf \colorbox{pink} {Ans.6}$

Suppose the present age of the son is X years. Then, the father's age at present is 5x years.

The son's age after 10 years will be (x+10) years. The father's age after 10 years will be (5x +10) years.

According to the problem.

$5x + 10 = 3(x + 10) \:$

‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎OR

$5x + 10 = 3x + 30$

‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎OR

$5x - 3x = 30 - 10$

‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎OR

$2x = 20 \: \: or \: \: x = \frac{20}{2} = 10$

Therefore The Age of the son is 10 Years and the present age of the father is

$5 \times 10 \: years = 50 \: years$

$\sf \colorbox{pink} {\sf \colorbox{pink} {Ans.7}}$

Let x and x+5 be the two consecutive positive integers .

$Therefore \: x \: (x+1) =306.$

‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎OR

$\frac{x}{2} + x - 306 = 0$

‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎OR

$\frac{x}{2} + (18 - 17)x - 306 = 0$

‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎OR

$(x + 18)(x - 17) = 0$

‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎‎ ‎

$We \: get x =17,and -18.</strong></p><p><strong>[tex]We \: get x =17,and -18.$

Therefore the two consecutive positive integers are 17 and 18.

$\\ \\ \\ \sf \colorbox{gold} {\red(ANSWER ᵇʸ ⁿᵃʷᵃᵇ⁰⁰⁰⁸}$