Question

the ratio of the number of apples to oranges in a basket were 2:5. some fruits of one kind were added to the basket and the ratio of apples to oranges changed to 4:7. which fruit was added to the basket??

Answer 1

Answer
Let first apple = x
And oranges = y

As we know $\frac{x}{y}=\frac{2}{5}$

Now assume we add some apples as z .

So our ratio = $\frac{x+z}{y}=\frac{4}{7}$

$\Rightarrow$ $\frac{x}{y}+\frac{z}{y}=\frac{4}{7}$

we know ( $\frac{x}{y}=\frac{2}{5}$ )

$\Rightarrow$ $\frac{z}{y}=\frac{4}{7}-\frac{2}{5}$

$\Rightarrow$ $\frac{z}{y}$ = $\frac{6}{35}$

Now lets assume we add some oranges than we get
$\frac{x}{y+z}=\frac{4}{7}$

$\Rightarrow$$\frac{y}{x}+\frac{z}{x}=\frac{7}{4}$

$\Rightarrow$ $\frac{z}{x}$ = $\frac{7}{4}$ - $\frac{5}{2}$

$\Rightarrow$ $\frac{z}{x}$ = - $\frac{3}{4}$
As we can see that if we add oranges our ration is in negative that is not possible so
We add apples (Ans)