Question

the product of two successive multiples of 10 is 1200 . then find these multiples.​

Answer 1

$\huge\underline \color{gold}ANSWER$

Let the 2 multiples of 10 be 10x and 10x+10

According to the problem,

$10x(10x+10) = 1200 \\ = 100x(x+1) = 1200 \\ = x(x+1) = 12 \\ = {x}^{2} + x - 12 = 0 \\ = {x}^{2} + 4x - 3x - 12 = 0 \\ = (x + 4)(x - 3) = 0 \\ x = - 4 \: or \: + 3$

CASE 1

When x = - 4

10x = - 40

10x + 10 = -30

10x(10x+10) =-40(-30)= 1200

CASE 2

When x = - 3

10x = - 30

10x + 10 = -20

10x(10x+10) = -30(-20)=600

THEREFORE, CASE 1 IS CORRECT ✅

Answer 2

Solution :

Let the two successive multiples be 10k and 10 l respectively where l = k + 1 .

Now , it is given that the product is 1,200 .

So ,

10k × 10l = 1200

=> 100 kl = 1200

=> kl = 12

l = k + 1

=> k ( k + 1) = 12

=> k² + k = 12

=> k² + k - 12 = 0

=> k² + 4k - 3k - 12 = 0

=> k ( k + 4 ) - 3( k + 4 ) = 0

=> ( k - 3)( k + 4) = 0

k = 3 or -4

If k = 3

l = 4

Multiples are 30 and 40 respectively .

If k = -4

l = -3

Multiples are -30 and -40 respectively .

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