Question

The product of 4 consecutive numbers which are multiples of 5. is 15,000. Find the natural nos.

Answer 1

It is

5 multiplied by 10 multiplied by 15 multiplied by 20

Answer 2

(x – 5) (x) (x + 5) (x + 10) = 15000
∴ x ( x + 5 ) (x – 5 )( x + 10 ) = 15000
∴ (x2 + 5x) (x2 + 10x – 5x – 50) = 15000
∴ (x2 + 5x) (x2 + 5x – 50) = 15000
Put, x2 + 5x = m
∴ m ( m – 50 ) = 15000
∴ m2 – 50 m = 15000
∴ m2 – 50m – 15000 = 0
m2 – 150m + 100m – 15000 = 0
∴ m (m – 150) + 100 (m – 150) = 0
∴ (m – 150) ( m + 100) = 0
∴ m – 150 = 0    OR  m + 100 = 0
∴ m = 150  OR  m = - 100  
∵ Natural Numbers can't be negative,
∴ m ≠ - 100  But m = 150
Now re – substituting,
m = x2 + 5x

m = 150∴ x2 + 5x = 150∴ x2 + 5x – 150 = 0∴ x2 +15x – 10x – 150 = 0∴ x(x + 15 ) – 10 (x + 15) = 0∴ (x + 15) (x – 10) = 0∴ x + 15 = 0   OR  x – 10 = 0∴ x = -15   OR  x = 10
∵ Natural Number can't be negative∴ x ≠ - 15 But x = 10
∴ x – 5 = 10 – 5 = 5∴ x = 10∴ x + 5 = 10 + 5 = 15∴ x + 10 = 10 + 10 = 20