Question

Anil's father is 26 years younger than Anil’s grandfather and 29 years older than anil. The sum of the ages of all the three is 135 years. What is the age of each one of them? *

2 points

Anil’s age:18 yr; Anil’s father’s age: 45 yr ;Anil's grandfather’s age = 72 yr

Anil’s age:72 yr; Anil’s father’s age: 46 yr ;Anil's grandfather’s age = 17 yr

Anil’s age:17 yr; Anil’s father’s age: 46 yr ;Anil's grandfather’s age = 72 yr

Anil’s age:45 yr; Anil’s father’s age: 17 yr ;Anil's grandfather’s age = 72​

Answer 1

$\:\frak{Given}\:\begin{cases} \:\quad \sf \:Grandfather's\: age \:=\: \pmb{\sf{ \:Father's \:Age \:+\:26\:}}\\\\ \:\quad \sf \:Anil's\: age \:=\: \pmb{\sf{ \:Father's \:Age \:-\:29\:}}\\\\ \:\quad \sf Father's \:Age\:+\:Anil's\:Age\:+\: Grandfather's\:age\:=\:\pmb{\sf{ 135\:}}\end{cases}\:$

Need To Find : Age of Anil , Anil's Father and Anil's Grandfather ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that age of Father be x yrs . Then , Grandfather's age will be ( x + 26 ) yrs and Anil's age will be (x - 29 ) yrs .

$\\\qquad \:\:\bigstar \:\:\underline {\pmb{\pink {\sf \: According \:To\:The \:Question \:\::\:}}}\:$

⠀⠀⠀▪︎⠀The sum of the ages of all the three is 135 years .

$\\ \dashrightarrow \sf \big\{ Father's \:Age \:\big\} \:+\:\big\{ Grandfather's \:Age \:\big\} \:+\:\big\{ Anil's \:Age \:\big\} \:=\:135\:\\\\\\ \dashrightarrow \sf \big\{ x \:\big\} \:+\:\big\{ x + 26\:\big\} \:+\:\big\{ x - 29 \:\big\} \:=\:135\:\\\\\\ \dashrightarrow \sf x \: \:+\: x + 26\:+\: x - 29 \:=\:135\:\\\\\\ \dashrightarrow \sf x \: \:+\: x + x\:+\: 29 - 26 \:=\:135\:\\\\\\ \dashrightarrow \sf 3x\:+\: 26 - 29 \:=\:135\:\\\\\\ \dashrightarrow \sf 3x\:+\: 3 \:=\:135\:\\\\\\ \dashrightarrow \sf 3x\: \:=\:135\:+\:3\:\\\\\\ \dashrightarrow \sf \:x\: \:=\:\dfrac{138}{3}\:\\\\\\ \dashrightarrow \pmb {\underline {\boxed {{\:\frak{ \:x\:\:=\:46\:yrs\:}}}}}\:\bigstar \:$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

$\qquad \dag \underline {\frak{\:Therefore \:,\: Their \:ages\:are\::\:}}$

• Anil's Father Age , x = 46 yrs ,
• Anil's Grandfather Age , x + 26 = ( 46 + 26 ) = 72 yrs &
• Anil's Age , ( x - 29 ) = ( 46 - 29 ) = 17 yrs .