The sum of two numbers is equal to sum of square of 12 and cube of 6. The smaller number is 21 less than the square of 9. The difference of 5 times the smaller number and fifty percent of larger number is -

The Correct answer is Option 3. 

Key Points

Let the larger and smaller numbers be x and y respectively.

Now,

x + y = 12² + 6³ = 144 + 216 = 360 ...(i)

Again,

y = 9² – 21 = 81 – 21 = 60

From equation (i), we get:

x = 360 – 60 = 300

Now, required value = 5y – 50% of x

= 5 × 60 – 50% of 300

= 300 – 150 = 150

Thus, the difference of 5 times the smaller number and fifty percent of larger number is half of the larger number.

Hence, option (c) is correct.