Question

three prizes are to be distributed in a quiz contest.The value of the 2nd prize is five-sixths the value of the first prize and the value of the third prize is four-fifths that of the 2nd prize.If the total value of the three prizes is rs.150,Find the value of each prize​

Answer 1

Answer:

1 = 60

2= 50

3= 40

Step-by-step explanation:

let value of 1st= x

2 nd = (5/6)x

3rd= (4/5)× 2nd

1st+2nd+3rd= 150

on solving x, we get x=60

Answer 2

$\bf \pink{Given,}$

• Total no. prize (3)
• The total money of prize ( ₹ 150 )
• Value of 2nd prize ( 5/6 of the 1st prize )
• Value of 3rd prize ( 4/5 of 2jd prize )

$\bf \pink{To \: find ,}$

Value of each prize.

$\bf \pink{How \: to \: find :-}$

By assuming the cost of first prize as x and 2nd prize $\bf \frac{5}{6}x$ and 3rd prize $\bf \frac {4}{5} \times \frac{5}{6}x$ and ₹150 total of all prize , we will equate this... information and will get the price of 1st prize and by that we can find the rest ones.

$\bf \red{Solution :- }$

Total cost = ₹ 150

Let the price of 1st prize be ₹x ,2nd prize $\bf \frac{5}{6}x$ and 3rd prize $\bf \frac {4}{5} \times \frac{5}{6}x$

A/Q

$\implies \sf \: x + \frac{5}{6} x + \frac{ \cancel{4}_2}{ \cancel5} \: \times \frac{ \cancel5}{ \cancel6} _ 3 \: x = 150 \red{ [equating \: both \: sides]}\\ \implies \sf \: x \: + \frac{5}{6} x + \frac{2}{3} x = 150 \\ \sf \implies \: \frac{6x + 5x + 4x}{6} = 150 \\ \sf \implies \: \frac{15}{6} x = 150 \\ \sf \implies \: 15x = 150 \times 6 \\ \sf \implies15x = 900 \\ \sf \implies \: x = \frac{ \cancel{900} \: _{60}}{ \cancel{15}} \\ \sf \pink{ \therefore}x = 60 \: \:$

So,

The cost of 1st prize = x = ₹60

The cost of 2nd prize = $\sf \: \frac{5}{6} x = \frac{5}{ \cancel6} \times \cancel{60} \: _{10} = ₹ 50$

The cost of 3rd prize = $\sf \frac{2}{3} x = \frac{2}{ \cancel3} \times \cancel{ 60 } \: _{20} = ₹ 40$

Hence solved $\huge \red ✓$

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If you want to check the ans...then add the Answer.

₹60+₹50+₹40 = ₹150

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm checked \: \red✓$

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