the total cost of three prizes is 2550 if the value of the second prize is 3 by 4 ths of the first and the value of the third prize is 1 by 2 of the first prize find the value of the first prize
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The total cost of three prizes is Rs. 2550. If the value of the second prize is 34th of the first and the value of the 3rd prize is 12 of the second prize. Find the value of the first prize.
A. Rs. 900
B. Rs. 1500
C. Rs. 1200
D. Rs. 450
Answer
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Hint: In this, we have to form a linear equation in one variable by assuming the value of first prize and then applying the conditions given to us.
A linear equation is of the form ax+b=0, where a and b are constants and x is a variable.
Complete step-by-step answer:
Given that the total cost of three prizes is Rs. 2550. We assume that the cost of first prize is x.
Then, according the given condition,
Value of second prize = 34th of the first prize = 34×x=3x4
Also, value of third prize = 12 of the second prize = 12×\Rightarrow3x4=3x8
Now, since, the total value of all the three prizes is Rs. 2550. Thus,
⇒ x+3x4+3x8=2550
Taking LCM in denominator, we get,
⇒ 8x+6x+3x8=2550
Cross multiplying, we get,
⇒ 8x+6x+3x=8×2550
Solving this, we get,
⇒ 17x=20400
⟹x=2040017=1200
Thus, the value of first prize is Rs. 1200.
Answer:
1200
Step-by-step explanation