Question

The present age of Ram's father is three times the present age of Ram. After six years the sum of their ages will be 73 years. Find the present age of Ram.

Answer 1

Correct Question :

The present age of Ram's father is three times the present age of Ram. After six years the sum of their ages will be 72 years. Find the present age of Ram.

(Because if I take sum of their ages 73 then their ages came in fraction which is not possible)

Solution :

Let present age of Ram's father be "F" years and present age of Ram be "R" years.

The present age of Ram's father is three times the present age of Ram.

According to question,

=> F = 3 × R

=> F = 3R _____ (eq 1)

After six years, the sum of their ages will be 72 years.

Now,

• Age of Ram's father = (F + 6) years.
• Age of Ram = (R + 6) years.

According to question,

=> F + 6 + R + 6 = 72

=> F + R + 12 = 72

=> 3R + R = 72 - 12 [From (eq 1)]

=> 4R = 60

=> R = 60/4

=> R = 15

Put value of R in (eq 1)

=> F = 3(15)

=> F = 45

∴ Present age of Ram is 15 years and present age of Ram's father is 45 years.

______________________________

✯ Verification :

From above calculations we have R = 15 and F = 45

According to question we have equations :

1) F = 3R

2) F + 6 + R + 6 = 72

Put value of R and F in (eq 1)

=> 45 = 3(15)

=> 45 = 45

Similarly, put value of R and F in (eq 2)

=> 45 + 6 + 15 + 6 = 72

=> 72 = 72

Answer 2

Answer:

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$to \: find \: = \: the \: present \: age \: of \: ram.$

$suppose \: the \: age \: of \: ram \: = x.$

$and \: the \: age \: of \: ram \: father \: = b.$

$the \: present \: age \: of \: rams \: father \: is \: 3 \: times \: the \: present \: age \: of \: ram \: .$

$b \: = 3 \times x$

$b \: = 3x....(1)$

$after \: 6 \: years \: the \: sum \: of \: their \: ages \: will \: be \: = \: 72 \: years.$

$ram(x \: + 6) \: years.$

$ram \: father \: = (b \: + \: 6)years.$

$b \: + \:6 \: + \: x\: + \: 6 \: = \: 72$

$b \: + x \: + \: 12 = 72.$

$3x \: + \: x \: + \: = \: 72 \: - 12.$

$4x \: = 60.$

$x \: = \frac{60}{4}$

$x \: = 15$

$value \: of \: x \: in \: equation \: ....(1)$

$b \: = 3(15).$

$b \: = 45.$

$the \: present \: age \: of \: ram \: = 15$

$the \: present \: age \: of \: ram \: father \: = 45 \: years.$