Correct Answer - Option 3 : $ 500
Given:
Total money divided $1200 among the three.
Elan gets half of the total amount received by Vill and Mark.
Vill gets one-third of the total amount received by Elan and Mark.
Formula Used:
If A invest Rs. x for p months and B invest Rs.y for q months then,
(A's share) : (B's share) = xp : yq
Basic Knowledge of Linear equations.
Calculation:
Let the amount to be received by Elan, Vill and Mark be p, q and r.
So, p + q + r = 1200
p = 1/2 (q + r)
⇒ 2p = q + r ----(1)
Add p both the sides
⇒ 3p = p + q + r
⇒
3p = 1200
⇒ p = $ 400
q = 1/3 (p + r)
⇒ 3q = p + r
Add 'q' both the sides,
⇒ 4q = p + q + r
⇒ 4q = p + q + r
⇒ 4q = 1200
⇒ q = $ 300
r = 1200 -( p + q) = 1200 - (400 + 300) = 1200 - 700 = $ 500
∴ Mark received a amount of $ 500.
