Reverse percentages Worked Solutions — GCSE Maths

Decide what the given amount stands for

The $20\%$ was taken off the original, not taken off $\pounds 48$. So $\pounds 48$ is $80\%$ of the original — this is a reverse percentage problem, and the original is the number we have to find.

Divide by the multiplier

$80\%$ as a decimal multiplier is $0.8$. The original was multiplied by $0.8$ to get $\pounds 48$, so dividing by $0.8$ undoes it and gives $\pounds 60$.

Check by working forwards

The round-trip check: $\pounds 60$ with the change applied gives $\pounds 48$, exactly as the question says. (Doing $\pounds 48 \times 1.2 = \pounds 57.60$ instead would be wrong — the $20\%$ was a percentage of the original, not of $\pounds 48$.)

Decide what the given amount stands for

The $10\%$ was taken off the original, not taken off $\pounds 45$. So $\pounds 45$ is $90\%$ of the original — this is a reverse percentage problem, and the original is the number we have to find.

Divide by the multiplier

$90\%$ as a decimal multiplier is $0.9$. The original was multiplied by $0.9$ to get $\pounds 45$, so dividing by $0.9$ undoes it and gives $\pounds 50$.

Check by working forwards

The round-trip check: $\pounds 50$ with the change applied gives $\pounds 45$, exactly as the question says. (Doing $\pounds 45 \times 1.1 = \pounds 49.50$ instead would be wrong — the $10\%$ was a percentage of the original, not of $\pounds 45$.)

Decide what the given amount stands for

The $25\%$ was taken off the original, not taken off $\pounds 36$. So $\pounds 36$ is $75\%$ of the original — this is a reverse percentage problem, and the original is the number we have to find.

Divide by the multiplier

$75\%$ as a decimal multiplier is $0.75$. The original was multiplied by $0.75$ to get $\pounds 36$, so dividing by $0.75$ undoes it and gives $\pounds 48$.

Check by working forwards

The round-trip check: $\pounds 48$ with the change applied gives $\pounds 36$, exactly as the question says. (Doing $\pounds 36 \times 1.25 = \pounds 45$ instead would be wrong — the $25\%$ was a percentage of the original, not of $\pounds 36$.)

Decide what the given amount stands for

The $10\%$ was added on to the original, not added on to $\pounds 55$. So $\pounds 55$ is $110\%$ of the original — this is a reverse percentage problem, and the original is the number we have to find.

Divide by the multiplier

$110\%$ as a decimal multiplier is $1.1$. The original was multiplied by $1.1$ to get $\pounds 55$, so dividing by $1.1$ undoes it and gives $\pounds 50$.

Check by working forwards

The round-trip check: $\pounds 50$ with the change applied gives $\pounds 55$, exactly as the question says. (Doing $\pounds 55 \times 0.9 = \pounds 49.50$ instead would be wrong — the $10\%$ was a percentage of the original, not of $\pounds 55$.)

Decide what the given amount stands for

The $20\%$ was added on to the original, not added on to $\pounds 96$. So $\pounds 96$ is $120\%$ of the original — this is a reverse percentage problem, and the original is the number we have to find.

Divide by the multiplier

$120\%$ as a decimal multiplier is $1.2$. The original was multiplied by $1.2$ to get $\pounds 96$, so dividing by $1.2$ undoes it and gives $\pounds 80$.

Check by working forwards

The round-trip check: $\pounds 80$ with the change applied gives $\pounds 96$, exactly as the question says. (Doing $\pounds 96 \times 0.8 = \pounds 76.80$ instead would be wrong — the $20\%$ was a percentage of the original, not of $\pounds 96$.)