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The Product of Four Consecutive Natural Numbers, Which Are Multiples of Fives, Is Rs. 15,000. Find Those Natural Numbers. - Algebra

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The product of four consecutive natural numbers, which are multiples of fives, is Rs. 15,000. Find those natural numbers.

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Solution

Let 5x, 5(x+1), 5(x+2) and 5(x+3) be four consecutive natural numbers, which are multiple of fives. 
It is given that product of these consecutive numbers is 15000.

5𝑥×5(𝑥+1) ×5 (𝑥+2) ×5( 𝑥+3) = 15000

625×𝑥( 𝑥+1)( 𝑥+2)( 𝑥+3) =15000

𝑥 (𝑥+1)( 𝑥+2)( 𝑥+3) =15000/625

𝑥 (𝑥+1)( 𝑥+2)( 𝑥+3) =24

When 𝑥=1 Then,

𝑥 (𝑥+1)( 𝑥+2)( 𝑥+3)

1 (1+1)( 1+2)( 1+3)

1(2)(3)(4) =24

Hence, the four consecutive natural numbers are

5𝑥=5×1=5

5 (𝑥+1) =5× (1+1) =5×2=10

5 (𝑥+2) =5× (1+2) =5×3=15

5 (𝑥+3) =5× (1+3) =5×4=20

Therefore four consecutive natural numbers are 5, 10, 15 and 20.

Concept: Linear Equations in Two Variables Applications
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