# If the ratio of two numbers is 3:5 and their sum is 360, then the numbers are 135 and 225

If true then enter 1 and if false enter 0

Last updated date: 23rd Mar 2023

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Answer

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Hint: We can assign a variable to the two numbers and form equations to find these variables.

First we will assume the two numbers to be x and y.

Complete step by step answer:

Now we will proceed with the question sequentially and form equations so we can find x and y.

The ratio of two numbers is 3:5 $\Rightarrow $ $x:y=3:5$

Now we know that ratios can also be written as divisions. Therefore, we can write

$\dfrac{x}{y}=\dfrac{3}{5}$

Multiplying both sides with $\dfrac{5}{3}$ we have

$\dfrac{5}{3}.\dfrac{x}{y}=\dfrac{5}{3}.\dfrac{3}{5}$

On simplification we get,

$\dfrac{5x}{3y}=1$

$\Rightarrow 5x=3y$

Therefore, we can write

$x=\dfrac{3}{5}y$ (i)

Now we have one equation. We need one more to find x and y.

The second statement of the question says,

The sum is 360 $\Rightarrow $ $x+y=360$ (ii)

After substituting the value of x from equation (i) in equation (ii) we have,

$\dfrac{3}{5}y+y=360$

Taking 5 as LCM we have,

$\dfrac{3y+5y}{5}=360$

$\Rightarrow \dfrac{8y}{5}=360$

Multiplying both sides with 5 we have,

$8y=360\times 5$

Multiplying both sides with 8 we have,

$y=\dfrac{360\times 5}{8}$

On calculating y we have,

$y=225$

Now that we have calculated y we can also calculate x from equation (ii)

$x+y=360$

$\Rightarrow x=360-y$

On substituting value of y we have,

$\Rightarrow x=360-225$

$\Rightarrow x=135$

Therefore, the numbers are 225 and 135.

Hence, the answer is 1.

Note: The only source of error here can be misreading the question and writing the wrong equations. One more thing to keep in mind is that we can write $x:y=\dfrac{x}{y}$ but we cannot write $x:y:z=\dfrac{\dfrac{x}{y}}{z}$ . It only applies when there are only two terms.

First we will assume the two numbers to be x and y.

Complete step by step answer:

Now we will proceed with the question sequentially and form equations so we can find x and y.

The ratio of two numbers is 3:5 $\Rightarrow $ $x:y=3:5$

Now we know that ratios can also be written as divisions. Therefore, we can write

$\dfrac{x}{y}=\dfrac{3}{5}$

Multiplying both sides with $\dfrac{5}{3}$ we have

$\dfrac{5}{3}.\dfrac{x}{y}=\dfrac{5}{3}.\dfrac{3}{5}$

On simplification we get,

$\dfrac{5x}{3y}=1$

$\Rightarrow 5x=3y$

Therefore, we can write

$x=\dfrac{3}{5}y$ (i)

Now we have one equation. We need one more to find x and y.

The second statement of the question says,

The sum is 360 $\Rightarrow $ $x+y=360$ (ii)

After substituting the value of x from equation (i) in equation (ii) we have,

$\dfrac{3}{5}y+y=360$

Taking 5 as LCM we have,

$\dfrac{3y+5y}{5}=360$

$\Rightarrow \dfrac{8y}{5}=360$

Multiplying both sides with 5 we have,

$8y=360\times 5$

Multiplying both sides with 8 we have,

$y=\dfrac{360\times 5}{8}$

On calculating y we have,

$y=225$

Now that we have calculated y we can also calculate x from equation (ii)

$x+y=360$

$\Rightarrow x=360-y$

On substituting value of y we have,

$\Rightarrow x=360-225$

$\Rightarrow x=135$

Therefore, the numbers are 225 and 135.

Hence, the answer is 1.

Note: The only source of error here can be misreading the question and writing the wrong equations. One more thing to keep in mind is that we can write $x:y=\dfrac{x}{y}$ but we cannot write $x:y:z=\dfrac{\dfrac{x}{y}}{z}$ . It only applies when there are only two terms.

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