Question

The question in which I am facing problem is :

Three prizes are to be distributed in a quiz contest. The value of second prize is 5/6 of the value of first prize and the value of third prize is 4/5 of second prize. If the total value of three prizes is Rs.1500. Find the value of each prize. (in order of 1st, 2nd & 3rd

The solution which was given to me was:

Let the value of first prize = x

Value of second prize = 56x

Value of third prize = 45 (Value of the second prize)

= 45 (56x) = 23x

Total value of three prizes = Rs.1500

⇒x+56x+23x=1500
⇒ 6x+5x+4x6=1500
⇒ 15x6=1500
⇒x=600
Value of first prize = Rs. 600
Value of second prize = 56 × Rs. 600 = Rs. 500
Value of third prize = 23 × Rs. 600 = Rs. 400

Now, my doubt is that why was 2/3x taken in the equation ? It was not mentioned in the question

Answer 1

Let the value of first prize = x

Value of second prize = 5/6x

Value of third prize = 4/5 (Value of the second prize)

= 4/5 (5/6x) = 2/3x

So third price is 2/3 times of first price

Total value of three prizes = Rs.1500

⇒x+5/6x+2/3x=1500
⇒ 6x+5x+4x6=1500
⇒ 15x6=1500
⇒x=600
Value of first prize = Rs. 600
Value of second prize = 56 × Rs. 600 = Rs. 500
Value of third prize = 23 × Rs. 600 = Rs. 400

As I mentioned above the third price is 4/5 times of second price and 2/3 times of the first price