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प्रश्न
In a Mathematics quiz, 30 prizes consisting of 1st and 2nd prizes only are to be given. 1st and 2nd prizes are worth ₹ 2000 and ₹ 1000, respectively. If the total prize money is ₹ 52,000 then show that:
- If 1st prizes are x in number the number of 2nd prizes are ______.
- The total value of prizes in terms of x are ______.
- The equation formed is ______.
- The solution of the equation is ______.
- The number of 1st prizes are ______ and the number of 2nd prizes are ______.
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उत्तर
- If 1st prizes are x in number the number of 2nd prizes are 30.
- The total value of prizes in terms of x are 2000x + 1000(30 – x).
- The equation formed is 1000x + 30000 = 52000.
- The solution of the equation is x = 22.
- The number of 1st prizes are 22 and the number of 2nd prizes are 8.
Explanation:
Given, the number of prizes = 30
Total prize money = ₹ 52000, 1st and 2nd prizes are worth ₹ 2000 and ₹ 1000, respectively.
a. 1st prizes are x in number, the number of 2nd prizes are (30 – x), because total number of prizes are 30.
b. Total value of prizes in terms of x are 2000x + 1000(30 – x).
c. The equation formed is 1000x + 30000 = 52000
From (b), 2000x + 1000(30 – x) = 52000
⇒ 2000x + 30000 – 1000x = 54000
⇒ 1000x + 30000 = 52000
d. The solution of the equation is 22.
From (c), 1000x + 30000 = 52000
⇒ 1000x = 52000 – 30000 = 22000
⇒ x = `22000/1000` = 22
e. From (b), 2000x + 1000(30 – x) = 52000
2x + (30 – x) = 52 ...[Dividing both sides by 1000]
x + 30 = 52
⇒ x = 52 – 30 = 22
∴ Number of 2nd prizes = 30 – 22 = 8
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