There are 16 more apples than oranges in a basket of 62 apples and oranges

Answer: 24

Using equivalent ratios

Using multiples

At the beginning, there are 8 oranges for every 3 apples, so the number of oranges must be a multiple of 8. At the end, there are 3 oranges for every apple, so the number of oranges must be a multiple of 3. The number of oranges does not change, so it must be a multiple of 8 and a multiple of 3. Common multiples of 3 and 8 are 24, 48, ... so we could try these as the number of oranges. 3 : 8 is equivalent to 9 : 24 1 : 3 is equivalent to 8 : 24 9 $-$ 1 = 8, so there were 9 apples and 24 oranges to begin with.

Using algebra

Let $a$ be the number of apples and $o$ be the number of oranges at the beginning. Then we have that the ratio $a:o$ is $3:8$ and the ratio $a-1:o$ is $1:3.$ These give the simultaneous equations $8a=3o$ and $3(a-1)=o\Rightarrow 3a-3=o$

Solving by elimination

Multiplying both sides of $3a-3=o$ by $3$ gives $9a-9=3o$. Subtracting the equation $8a=3o$ from $9a-9=3o$ gives $$\begin{align}9a-9-8a&=3o-3o\\\Rightarrow a-9&=0\\\Rightarrow a&=9\end{align}$$ Substituting $a=9$ into $3a-3=o$ gives $o=3\times9-3=24.$

Solving by substitution

Substituting $o=3a-3$ into $8a=3o$ gives $$\begin{align}8a&=3(3a-3)\\ \Rightarrow8a&=9a-9\\ \Rightarrow0&=a-9\\ \Rightarrow9&=a\end{align}$$ Substituting $a=9$ into $3a-3=o$ gives $o=3\times9-3=24.$

There will be 28 apples and 24 oranges; 52 - 4 = 48 ← this is now double the number of the fewer fruit 48 / 2 = 24 ← the number of the fewer fruit 24 + 4 = 28 ← the number of the fruit of which there are more 28 + 24 = 52 ← a check of the answer.

In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation.