Question

Three prize are to be distributed in a debating contest.फ्री प्राइस r2b डिस्ट्रीब्यूटर इन ​

Answer 1

$\bf \purple { \underline { \sf Given :- }}$

• The total prize distributed ₹1500.
• Tha value of second prize is five-sixth i.e., 5/6 of first prize.
• And, the value of third prize is four-fifths i.e., 4/5 that of second one i.e., 5/6

$\sf \orange { \underline { \sf To \: find :- }}$

• The amount of three prize distributed.

$\sf \red { \underline { \sf Solution :- }}$

• Let's assume that the value of first prize is ₹x therefore prize of the second one will be ₹5x/6 and the prize of third one will be 4/5 of 5x/6 i.e., ₹2x/3.

According to the question,

• The sum of their prize is ₹1500.

$\bf \therefore \: \frac{5x}{6} + \frac{2x}{3} + x = 1500 \\ \bf \implies \: \frac{5x + 4x + 6x}{6} = 1500 \\ \bf \implies \: \frac{15x}{6} = 1500 \\ \bf \implies \: 15x = 1500 \times 6 \\ \bf \implies \: x = \frac{ \cancel{1500} \times 6}{ \cancel{15}} \\ \bf \implies \: x \: = 100 \times 6 \\ \bf \implies \:{ \underline{ \boxed{ \bf{ x \: = \: 600}}}}$

Hence,

• The first prize is x = ₹600.
• The second prize is 5x/6 of ₹600 = ₹500.
• The prize of third one is 2x/3 = ₹400.

$\mathfrak { \underline{ \green{ \purple V \red e \orange r \pink i \blue c \green a \orange t \red i \purple o \blue n: -}}}$

• As it is told that the sum of three prizes are ₹1500.
• Therefore, the prize we have found must be equal to ₹1500.

So,

Putting the value of the three prizes :-

$\bf \implies \: 500 + 600 + 400 = 1500 \\ \bf \implies \: 1500 = 1500 \\ { \underline{ \boxed{ \bf \therefore \: L.H.S \: = R.H.S}}}$

$\mathfrak { \underline{ \green{ Hence,\purple V \red e \orange r \pink i \blue f \green i \red e \pink d : -}}}$