Q. 24

Fill in the blanks to make the statements true.

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:

(a) If 1st prizes are x in number the number of 2nd prizes are ________.

(b) The total value of prizes in terms of x are ________.

(c) The equation formed is ________.

(d) The solution of the equation is ________.

(e) The number of 1st prizes are _______ and the number of 2nd prizes are ________.

Answer :

Given, number of prizes = 30


Total prize money = ₹52000, 1st and 2nd prizes are worth ₹2000 and ₹1000, respectively.


(a) 1st prize is 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 = 54000 – 30000


1000x = 24000


(d) The solution of the equation is 22.


From (c), 1000x + 30000 = 52000.


1000x = 52000 – 30000 = 22000


1000x = 22000



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