Mathematics
In a school, a class has 40 students out of which x are girls. If the product of the number of girls and number of boys in the class is 375; the number of boys in the class is :
15
25
15 or 25
15 and 25
Answer
Total students = 40
No. of girls = x
No. of boys = 40 - x
Given,
Product of number of girls and number of boys = 375
⇒ x(40 - x) = 375
⇒ 40x - x2 = 375
⇒ x2 - 40x + 375 = 0
⇒ x2 - 25x - 15x + 375 = 0
⇒ x(x - 25) - 15(x - 25) = 0
⇒ (x - 15)(x - 25) = 0
⇒ (x - 15) = 0 or (x - 25) = 0
⇒ x = 15 or x = 25.
If x = 15,
No. of boys = 40 - x = 40 - 15 = 25.
If x = 25,
No. of boys = 40 - x = 40 - 25 = 15.
Hence, Option 3 is the correct option.
Related Questions
In an auditorium, seats were arranged in rows and columns. The number of rows was equal to number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by 10, the total number of seats increased by 300. Find :
(i) the number of rows in the original arrangement.
(ii) the number of seats in the auditorium after re-arrangement.
A two digit number contains the largest digit at ten's place. The product of the digits is 27 and the difference between two digits is 6. Find the number.
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