GATE2018 CE-1: GA-3

Question

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?

• A. $14$
• B. $17$
• C. $18$
• D. $19$

Answer 1

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 $(D).$