# GATE2018 CE-1: GA-3

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Hema's age is $5$ years more than twice Hari's age. Suresh's age is $13$ years less than 10 times Hari's age. If Suresh is $3$ times as old as Hema, how old is Hema?

1. $14$
2. $17$
3. $18$
4. $19$

edited
Migrated from GO Civil 1 year ago by Arjun

Let Hema's age be $x,$ Hari's age be $y$ and Suresh's age be $z.$

According to the question:

• $x=5+2y\implies x-2y=5\qquad \to (1)$
• $z=10y-13\qquad \to (2)$
• $z=3x\qquad \to(3)$

From $(2)$ and $(3)$ we get

• $3x-10=-13\qquad \to(4)$

Solving equations $(1), \ (4)$ and $(3)$ we get $x=19,\ y=7$ and $z=57.$

Hema's age $x=19$

So, the correct answer is $(D).$

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Let's assume Hari's age is $x$ :

Hema = 5 more than the Twice of Hari's age  which means: $5+ 2x$ .......................equation $1$

Suresh = 13 years less than the 10 times's Hari's age which means : $10x - 13$

Suresh is 3 times as old as Hema which means : Suresh = 3[Hema],

Put he value of Suresh and Hema:

$10x- 13 = 3[ 5 +2x]$

$10x - 13 = 15 + 6x$

$10x- 6x = 15+13$

$4x= 28$

$x = 7$

put the value of x in equation 1 to get the value of Hema

hema = $5+2x$

Hema's age  = $5+2*7$

Hema's age $19$

right option - $D$

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