Question

How will the product change if: one factor is increased 3 times, and the other one is decreased 6 time

Answer 1

Algebra

The product will be reduced 2 times i.e the product will be reduced to half

Step-by-step explanation:

Let the product be $P_{1}$ and the two of its factors are a and b

So $P_{1}$ = $a_{1\\}$×$b_{1\\}$

Now if the factor $a_{1\\}$ is increased 3 times, then the new factor will be $a_{2}$

so $a_{2} = 3a_{1\\}$

The other factor $b_{1\\}$ is decreased 6 times, then the new factor will be $b_{2}$

so $b_{2 } = \frac{b_{1\\}\\}{6}$

So the new product $P_{2}$ = $a_{2} b_{2}$

⇒ $P_{2}$ = 3×$a_{1}$× $\\ \frac{b_{1\\}\\}{6}$

So  $P_{2} = \frac{P_{1}\\}{2}$

Hence, the product will be reduced 2 times i.e the product will be reduced to half