Question

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

Answer 1

Given :- The product of two successive multiples of 10 is 1200 . Then find these multiples ?

Solution :-

Let us assume that, first multiple of 10 is 10x and next multiple of 10 is 10y .

then,

→ First multiple * next multiple = 1200

→ 10x * 10y = 1200

→ 100xy = 1200

dividing both sides by 100,

→ xy = 12

Now,

• if x = 1, y = 12 => both are not consecutive numbers .
• if x = 2, y = 6 => both are not consecutive numbers .
• if x = 3, y = 4 => both are consecutive numbers .

Therefore,

→ First Multiple = 10x = 10 * 3 = 30

→ Next Multiple = 10y = 10 * 4 = 40 .

Hence, Required multiples are 30 and 40 respectively .

Note :-

As we know , if we multiply two negative numbers we get a positive number, since in question natural number is not mentioned , we can conclude that, given two successive multiples of 10 can be negative numbers also , which are (-30) and (-40) .

As,

• (-30) * (-40) = 1200 .

Therefore, Required multiples are also (-30) and (-40) respectively .

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Answer 2

SOLUTION

GIVEN

The product of two successive multiples of 10 is 1200

TO DETERMINE

The multiples

EVALUATION

Here it is given that The product of two successive multiples of 10 is 1200

Let us assume that the multiples are 10x and 10x + 10

So by the given condition

$\sf{10x(10x + 10) = 1200 \: }$

$\implies \sf{100x(x + 1) = 1200 \: }$

$\implies \sf{x(x + 1) = 12 \: }$

$\implies \sf{ {x}^{2} + x - 12 = 0 \: }$

$\implies \sf{ {x}^{2} + 4x - 3x - 12 = 0 \: }$

$\implies \sf{ x(x + 4) - 3(x + 4) = 0 \: }$

$\implies \sf{ (x + 4) (x - 3) = 0 \: }$

Which gives either x + 4 = 0 or x - 3 = 0

x + 4 = gives x = - 4

In this case the multiples are - 40 & - 30

Again x - 3 = 0 gives x = 3

In this case the multiples are 30 and 40

FINAL ANSWER

The required multiples are

- 40 & - 30

or

30 & 40

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