Sol.
Le the four consecutive natural numbers which are multiples of
five be x – 5, x, x + 5 and x + 10 respectively.
According to given condition,
∴ (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
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m = 150
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∴ x2 + 5x = 150
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∴ x2 + 5x – 150 = 0
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∴ x2 +15x – 10x – 150 = 0
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∴ x(x + 15 ) – 10 (x + 15) = 0
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∴ (x + 15) (x – 10) = 0
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∴ x + 15 = 0 OR
x – 10 = 0
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∴ x = -15 OR
x = 10
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∵ Natural Number can't be negative
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∴ x ≠ - 15 But x = 10
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∴ x – 5 = 10 – 5 = 5
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∴ x = 10
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∴ x + 5 = 10 + 5 = 15
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∴ x + 10 = 10 + 10 = 20
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∴ The
four consecutive natural numbers which are multiples of five are 5, 10, 15
and 20 respectively.
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