Question

it took 10 days for 30 painters to paint a big house. how long would it have taken for 10 painters to paint the house? A. Direct proportion B. Inverse proportion c. Partitive proportion d. Proportion ​

Answer 1

Answer:

The answer

is B. Inverse proportion

Answer 2

Given:

it took 10 days for 30 painters to paint a big house. how long would it have taken for 10 painters to paint the house?

To Find:

A. Direct proportion

B. Inverse proportion

C. Partitive proportion

D. Proportion ​

Solution:

To solve this kind of question we can use a direct formula that is

$\frac{M_{1}D_{1}H_{1}}{W_{1}} =\frac{M_{2}D_{2}H_{2}}{W_{2}}$

where,

          M= No of men

          D= No of days

          H= No of hours

          W= Total work

By using this any value can be easily found and according to this question we need only the M and D variable so let's put that in the equation

$M{_1}D_{1}=M_{2}D_{2}$

And using this formula we can see that and convert it into proportion we add a constant which goes as

$MD=constant$

So now we can add the proportionality sign because now we have a constant to deal with and converting it will go as,

$M\propto \frac{1}{D}$

So it is an inverse proportion relationship

Now we can also find the value of days required which goes as,

$10*30=10*x\\x=30days$

so it will take 30 days for 10 painters to complete the job

Hence, it is an inverse proportion and the correct option is (b).