A sum of ₹2,500 is distributed among X, Y and Z in the 1/2 : 3/4 : 5/6 ratio.

Question

A sum of ₹2,500 is distributed among X, Y and Z in the \(\frac 12:\frac 34:\frac 56\) ratio. What is the difference between the maximum share and the minimum share? 

(a) 300

(b) 350

(c) 400

(d) 450

Answer 1

Correct option is (c) 400

The ratio of  X, Y and Z = (1/2) : (3/4) : (5/6)

(1/2) : (3/4) : (5/6)

⇒ LCM of 2, 4, 6 is 12.

⇒ [(1/2) × 12] : [(3/4) × 12] : [(5/6) × 12]

⇒ 6 : 9 : 10

Let X gets be Rs. 6x

Y gets be Rs. 9x

Z gets be Rs.10x

According to the question:

 6x + 9x + 10x = 2500

⇒ 25x = 2500

⇒ x = 100

X gets = Rs. 6x = 6 × 100

⇒ Rs. 600

Y gets = Rs. 9x = 9 × 100

⇒ Rs. 900

Z gets = Rs.10 × 100

⇒ Rs. 1000

Now, difference between the maximum share and the minimum share = Rs. (1000 – 600)

⇒ Rs. 400

∴ The difference between the maximum share and the minimum share  Rs. 400.