Question

14. 11. Dhruvi's father is 28 years younger than Dhruvi's grandfather and 30 years older than Dhruvi. The sum the ages of all the three is 142 years. What is the age of each one of them?​

Answer 1

Given:

• Dhruvi's father is 28 years younger than Dhruvi's grandfather and 30 years older than Dhruvi.

• The sum the ages of all the three is 142 years.

To find:

• The age of each one of them.

To assume:

• Dhruvi's father age as d yrs

• Dhruvi's age as d - 30

• Dhruvi's grandfather age as d + 28

Solution:

From the question,

d +(d - 30) + (d + 28) = 142

=> 2d - 30 + d + 28 = 142

=> 3d - 30 + 28 = 142

=> 3d - 2 = 142

=> 3d = 142 + 2

=> 3d = 144

=> d = 144/3

=> d = 48

Therefore,

• Dhruvi's father age = d = 48yrs

• Dhruvi's age = d - 30 = 48 - 30 = 18yrs

• Dhruvi's grandfather age = d + 28 = 48 + 28 = 76yrs

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

↝ Dhruvi's father is 28 years younger than Dhruvi's grandfather and 30 years older than Dhruvi.

Let assume that

↝ Dhruvi's Father age be 'x' years

↝ Dhruvi's age be 'x - 30' years

↝ Dhruvi's grandfather age be 'x + 28' years.

So, we have

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Dhruvi's \: age \: = x - 30 \: years} \\ &\sf{Dhruvi's \: Father \: age \: = \: x \: years}\\ &\sf{Dhruvi's \: grandfather \: age = x + 28 \: years} \end{cases}\end{gathered}\end{gathered}$

Further given that,

↝ The sum the ages of all the three is 142 years.

$\rm :\longmapsto\:x + x - 30 + x + 28 = 142$

$\rm :\longmapsto\:3x - 2 = 142$

$\rm :\longmapsto\:3x = 142 + 2$

$\rm :\longmapsto\:3x = 144$

$\rm :\longmapsto\:x = \dfrac{144}{3}$

$\bf\implies \:x = 48$

Hence,

$\red{\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:\begin{cases} &\sf{Dhruvi's \: age \: = 18 \: years} \\ &\sf{Dhruvi's \: Father \: age \: = \: 48 \: years}\\ &\sf{Dhruvi's \: grandfather \: age = 76 \: years} \end{cases}\end{gathered}\end{gathered}}$