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

• $3x-10y=-13\qquad \to(4)$

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 $(D).$

Comments

Confused about step 4
it must be 10y not just 10

Answer 2

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 - $D$

Answer 3

Answer is D..
Hema = 2*Hari +5
Suresh = 10*Hari -13
Suresh = 3*Hema

just go with oprtions and crooscheck hema's age