After a 20\% increase followed by a 10\% decrease, a price is 108. What was the original price?

Worked solution for TMUA-P1-MNUM-030 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P1-MNUM-030 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P1-MNUM-030 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P1-MNUM-030?

No — calculators are banned in the TMUA. TMUA-P1-MNUM-030 is set for a no-calculator target of about 210 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P1-MNUM-030?

TMUA-P1-MNUM-030 is Paper P1 · Number (specification code M-Num), level 3. Drill more of the same topic from this page.

TMUA-P1-MNUM-030 — Paper P1 · Number · Level 3

P1M-NumLevel 3~210s target

Spec: M-Num · No calculator · ~210s

After a

20\%

increase followed by a

10\%

decrease, a price is

\pounds 108

. What was the original price?

Options

$\pounds 110$
$\pounds 98$
$\pounds 90$
$\pounds 120$
$\pounds 100$

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: mratio-reverse-percent, compound-change, reverse-percentage. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Work backwards through both multipliers: original

= 108 / (1.2 \times 0.9) = 108 / 1.08 = 100

, so

\pounds 100

.
Trap:

\pounds 98

nets

+20\%

and

-10\%

+10\%

— but successive changes multiply, they do not add.

Keep practising

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Keep practising

Same topic · same level

P1M-NumLevel 3

TMUA-P1-MNUM-011

4000 is invested. It grows by 5\% in year one, then falls by 5\% in year two. What is its final value?

Number

Open TMUA-P1-MNUM-011 →

Same trap: reverse-percentage

P1M-NumLevel 2

TMUA-P1-MNUM-008

After a 20\% increase, a jacket costs 60. What was its original price?

Number

Open TMUA-P1-MNUM-008 →

TMUA-P1-MNUM-030 — Paper P1 · Number · Level 3

Options

Keep practising

Master Number

TMUA-P1-MNUM-030 — Paper P1 · Number · Level 3

Options

Keep practising

Master Number