Question

The total cost of the three prizes is $Rs.2550$. If the value of the second prize is $\dfrac{3}{4}th$ of the first and the value of $3rd$ the prize is $\dfrac{1}{2}$ of the second prize;
Find the value of the first prize.
A. $Rs.900$
B. $Rs.1500$
C. $Rs.1200$
D. $Rs.450$

Answer 1

Hint: First we’ll assume the value of the first prize to be x, from that we’ll have the value of the second prize and then the value of the third prize, using the given conditions. Now we’ve given the value of the total sum of all three prizes, substituting the value of all prizes in that equation we’ll get the value of the first prize.

Complete step by step answer:
Given data: Total cost of 3 prizes$ = Rs.2550$
Value of second prize$ = \dfrac{3}{4}$ of the first prize
Value of third prize$ = \dfrac{1}{2}$ of the second prize
Let the value of first prize be x
Therefore, according to the given conditions
Value of second prize$ = \dfrac{3}{4}x$
And Value of the third prize$ = \dfrac{1}{2}\left( {\dfrac{3}{4}x} \right)$
$ = \dfrac{3}{8}x$
Now, we know that sum of all the three prizes$ = Rs.2550$
i.e. $x + \dfrac{3}{4}x + \dfrac{3}{8}x = 2550$
Now, taking the LCM of the denominator, we get,
$ \Rightarrow \dfrac{{8x}}{8} + \dfrac{{2 \times 3}}{{4 \times 2}}x + \dfrac{3}{8}x = 2550$
Now, simplifying the numerator as the denominator is the same, we get,
$ \Rightarrow \dfrac{{8x + 6x + 3x}}{8} = 2550$
$ \Rightarrow \dfrac{{17x}}{8} = 2550$
On cross multiplication, we get,
$ \Rightarrow x = \dfrac{{2550 \times 8}}{{17}}$
Dividing numerator and denominator with 17
$ \Rightarrow x = 150 \times 8$
$ \Rightarrow x = 1200$
Therefore, the value of the first prize$ = Rs.1200$
Hence, Option(C) is correct.

Note: In the given question it is mentioned that the third prize is $\dfrac{1}{2}$ of the second prize, but most of the students take $\dfrac{1}{2}$ of the first prize, so always go with the points mentioned in the question and follow them throughout the solution. Also as we were asked the value of first prize we have just calculated that, in other questions, it might be asked to find the value of others to prizes as well, so we simply substitute the value of x in other equations, to get the value of the second and third prize.