Question

The present age of saheel's mother is 3 times the present age of Sahil. After 5 years their ages will add to 66 years. Find their present ages.
1 point

Answer 1

$\sf\large\underline\blue{Let:}$

$\tt{\implies The\: present\:age\:_{(Saheel's\:mother)}=x}$

$\tt{\implies The\: present\:age\:_{(saheel)}=y}$

$\sf\large\underline\blue{To\: Find:}$

$\tt{\implies The\: present\:age\:_{(saheel\:and\:mother)}=?}$

$\sf\large\underline\blue{Solution:}$

• To calculate the present age of Saheel and his mother at first we have to set up equations as per the given clue in the question then solve those equation after that we get their parent age]

$\sf\small\underline\purple{Given\:in\:case\:(1):}$

• The present age of Saheel's mother is 3 times the present age of Sahil]

$\tt{\implies Mother's\:age=3\times\:of\:saheel's\:age}$

$\tt{\implies x=3y--------(1)}$

$\sf\small\underline\purple{Given\:in\:case\:(2):}$

• After 5 years their ages will be equal to 66 years.]

$\tt{\implies (x+5)+(y+5)=66}$

$\tt{\implies x+y+10=66}$

$\tt{\implies x+y=66-10}$

$\tt{\implies x+y=56------(2)}$

• Putting the value of x=3y in EQ (2) here:]

$\tt{\implies x+y=56}$

$\tt{\implies 3y+y=56}$

$\tt{\implies 4y=56\implies y=14}$

• Putting the value of y=14 in eq (2) ]

$\tt{\implies x+y=56}$

$\tt{\implies x+14=56}$

$\tt{\implies x=56-14\implies x=42}$

$\sf\large{Hence,}$

$\tt{\implies The\: present\:age\:_{(Saheel's\:mother)}=42\: years}$

$\tt{\implies The\: present\:age\:_{(Saheel)}=14\: years}$

Answer 2

$\bf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• The present age of saheel's mother is 3 times the present age of Saheel.
• After 5 years their ages will add to 66 years.

★ To find,

• Present age of Saheel and his mother.

★ Let,

$\sf\:\rightarrow Present\:age\:of\:Saheel's\:mother = a\:years.$

$\sf\:\rightarrow Present\:age\:of\:Saheel= b\:years.$

★ According to the question,

◼ The present age of saheel's mother is 3 times the present age of Saheel.

$\sf\:\rightarrow a = 3b ..... (1)$

◼ 5 years later, the sum of their ages = 66.

◼ 5 years later Saheel age = b + 5

◼ 5 years later his mother's age = a + 5.

★ Now,

$\sf\:\implies a + 5 + b + 5 = 66$

$\sf\:\implies a + b+10= 66$

$\sf\:\implies a + b= 66-10$

$\sf\:\implies a + b= 56$

• Substitute value of a.

$\sf\:\implies 3b + b= 56$

$\sf\:\implies 4b= 56$

$\sf\:\implies b= \cancel{\cfrac{56}{4}}$

$\sf\:\implies b = 14$

• Substitute value of b in (1).

$\sf\:\implies a = 3(14)$

$\sf\:\implies a = 42$

$\underline{\boxed{\rm{\purple{\therefore Present\:age\:of\:Saheel = 14\:years.}}}}\:\orange{\bigstar}$

$\underline{\boxed{\rm{\purple{\therefore Present\:age\:of\:Saheel's\:mother = 42\:years.}}}}\:\orange{\bigstar}$

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