Question

When ‘x + 5’ numbers having an average of 50 is added with ‘x + 15’ numbers having an average of ‘x + 10’, then average of all the numbers together becomes 50. Which of the following statements can be true such that
x > 5 x > 5 ?
I. The area of a square is ‘16x’ cm² and its perimeter is ‘1.6x’
cm.
II. When ‘x’ is subtracted from a positive number, then the number becomes 150 times of its reciprocal and if the number is divided by 6, then it becomes a perfect square.
III. When 1000 is divided by ‘x + 5’, then 10 is obtained as remainder.

Q: Answer-When ‘x + 5’ numbers having an average of 50 is added with ‘x + 15’ numbers having an average of ‘x...

According to question 50x 5 x 15x 10x 5 x 15 50 Or, 50x 250 x 25x 1502x 20 50 Or, x 75x 400 100x 1000 Or, x 25x 600 0 Or, x 40x 15 0 Or, x 40 For I Area 16 40 640, so side 810 cm. Perimeter 4 810 3210 cm. Value of 1.6x 1.6 40 64 cm. So, I cannot be true. For II Let the number be a. a 40 150a Or, a 40a 150 0 This does not give a suitable positive integer value of a. So, II cannot be true. For III Since, x 5 40 5 45 And, 1000 45 22 10 Therefore, remainder 10 So, III can be true. Hence, option c.