Aptitude · Percentages · Model 4

One percentage, one rupee figure, one division

Q: A man spends 30% on food and 3% in a trust, spending ₹2,310 on these two. Find his salary.

₹7,000. Here the rupee figure is the spending , not the savings: 33% is ₹2,310, so 1% is ₹70 and the salary is ₹7,000. Reading it as the leftover would give a completely different answer.

Somebody spends a list of percentages of their salary and you are told either what they spent or what they have left. Every question in this model is a single unitary step — the only decision is which percentage the rupee figure belongs to.

Set the shares and say which figure you were given →

Add the stated shares. Then decide whether the rupee figure you were given is that percentage or the leftover percentage. Everything else is one division.

01 The idea

The whole model is one unitary step

Radha spends 40% of her salary on food, 20% on rent, 10% on entertainment and 10% on conveyance, and saves ₹1,500. Those four shares are all percentages of the same salary, so they add to 80%. She therefore saves 20%, and 20% is ₹1,500, so the salary is ₹7,500.

That is the entire model. Add the percentages, work out which one your rupee figure corresponds to, and scale. There is no second idea, which is why these appear as thirty-second questions rather than as hard ones.

The only real decision is which percentage the money belongs to. If the question says “he spends 30% on food and 3% on charity, and spends ₹2,310 on these two”, then ₹2,310 is the 33% — not the leftover. If it says “after spending these he is left with ₹6,000”, the ₹6,000 is the 40% that survives. Both figures will be among the options.

The habit worth building is scaling through a tidy fraction rather than through 1%. Twenty per cent is a fifth, so ₹1,500 × 5 = ₹7,500 in one step. Exam percentages are chosen to be recognisable fractions precisely so this works — 33% is awkward, but 40%, 25%, 20% and 75% are not.

Decide whether your rupee figure is the part spent or the part left. That reading is the only thing this model tests.

Flat sharesPercentages all taken of the same salary, so they add. Contrast the remaining model, where each share is of what the previous one left.

The unitary stepFrom a known percentage and its value to the whole: total = value × 100 / that percentage.

Leftover percentage100 − (sum of the stated shares). What is saved when the question says “and saves the rest”.

02 Worked example

Four shares, ₹1,500 saved

The model in its standard form. Radha spends 40% of her salary on food, 20% on house rent, 10% on entertainment and 10% on conveyance. If her savings at the end of the month are ₹1,500, find her monthly salary.

Add the stated sharesAll four are percentages of the same salary, so they combine directly.40 + 20 + 10 + 10 = 80% spent

Find what is leftWhatever is not spent is saved.100% − 80% = 20% saved

Match the rupee figure to the right percentageThe ₹1,500 is described as savings, so it belongs to the 20% and not to the 80%.20% → ₹1,500

Scale up through the fractionTwenty per cent is one fifth, so the whole is five times the part.20% = 1/5 ⇒ salary = 1,500 × 5 = ₹7,500

Check it forwardsEighty per cent of the salary should be what she spent.80% of 7,500 = ₹6,000 spent, leaving ₹1,500 ✓

Note what the trap answer would have been: reading ₹1,500 as the 80% gives a salary of ₹1,875, which is less than what she supposedly spent — impossible, and catchable in a second. Whenever a reverse percentage answer comes out smaller than one of the parts, the rupee figure was matched to the wrong percentage.

03 The method

The variants, and the fractions worth recognising

Every version is the same division. The table is the shortcut list that makes it a mental calculation.

total = value × 100 / (the percentage that value represents). When the question names savings, that percentage is 100 − Σshares; when it names spending, it is Σshares itself.

Scale through the fraction, not through 1%. 20% is 1/5 so multiply by 5; 25% is 1/4 so multiply by 4; 40% is 2/5 so multiply by 5/2; 75% is 3/4 so multiply by 4/3. Going via 1% always works and takes two divisions; the fraction takes one multiplication. Where the percentage is genuinely awkward — 33% or 7% — go via 1% and accept it.

Percentage held	As a fraction	Multiply the value by
50%	`1/2`	`2`
40%	`2/5`	`5/2`
25%	`1/4`	`4`
20%	`1/5`	`5`
75%	`3/4`	`4/3`
12.5%	`1/8`	`8`
33% or 7%	`no tidy fraction`	go via 1%

05 Cheat sheet

Model 4 on one page

One division, and the reading that decides which division.

Case	Route	Worked
Savings given	`total = save × 100/(100−Σ)`	1,500 at 20% → 7,500
Spending given	`total = spend × 100/Σ`	2,310 at 33% → 7,000
Via one per cent	`value/pct, then ×100`	always works
Via the fraction	`value × reciprocal`	20% → × 5
Several items, one figure	`add the shares first`	35% + 5% = 40%
Annual from monthly	`× 12 at the end`	9,610 → 1,15,320
Matching the figure wrongly	`gives an impossible total`	smaller than a part

Read which percentage the money isSpending and savings are different percentages of the same salary, and both answers will be in the options. This is the only decision in the model.

An impossible total is a caught errorIf your salary comes out smaller than one of the amounts spent, you matched the rupee figure to the wrong percentage. Check before committing.

Scale through the fraction20% means multiply by 5; 25% means multiply by 4. One multiplication instead of two divisions, and exam percentages are chosen so it works.

06 Where & why

Where Model 4 shows up

The most-set percentage question in banking papers, and deliberately easy — it is there to be finished quickly.

Bank PO · SSC CGL · RRB

Salary and expenditure

One or two per paper. Thirty seconds each, and the trap is matching the rupee figure to the wrong percentage.

TCS NQT · Accenture

Several items summed

“35% on food and 5% on education, ₹17,600 on these two.” Add the shares first, then one division.

Multi-step versions

Monthly to annual, or a second investment

“7% is ₹2,170; he also invests 18% and 6% — find the annual total.” Find the salary, then the new percentage, then multiply by twelve.

Data interpretation

Pie charts

Every pie-chart question is this model: a sector percentage and one known value, giving the whole. The reading skill transfers exactly.

The only way to lose a mark here is to match the rupee figure to the wrong percentage. Underline whether the question says spends or is left with before you divide anything.

07 Interview questions

What gets asked

Nine, and they are all the same question with the reading changed.

A woman spends 40%, 20%, 10% and 10% of her salary and saves ₹1,500. Find the salary.

₹7,500. The four shares add to 80%, so she saves 20%, and 20% is ₹1,500. Twenty per cent is a fifth, so the salary is 1,500 × 5 = ₹7,500.

A man spends 30% on food and 3% in a trust, spending ₹2,310 on these two. Find his salary.

₹7,000. Here the rupee figure is the spending, not the savings: 33% is ₹2,310, so 1% is ₹70 and the salary is ₹7,000. Reading it as the leftover would give a completely different answer.

What is the one decision in this model?

Whether the rupee figure you were given is the amount spent on the stated shares or the amount left over. Those are different percentages of the same salary, and both resulting answers will be among the options.

How do you check the answer quickly?

Push it forwards: apply the spending percentage to your total and confirm the remainder matches. And sanity-check the size — if the salary comes out smaller than one of the amounts spent, you matched the figure to the wrong percentage.

A man spent ₹55,475 and ₹28,525, and has the remaining 25% as cash. Find the total.

₹1,12,000. The two amounts total ₹84,000, and if 25% remains then 75% was spent. So 75% is ₹84,000, making 1% equal ₹1,120 and the total ₹1,12,000. Note the spending was given as two rupee figures rather than as percentages.

Why scale through a fraction rather than through 1%?

Because it is one operation instead of two. Twenty per cent is a fifth, so multiply by 5 directly. Going via 1% needs a division and then a multiplication. Where the percentage has no tidy fraction — 33% or 7% — go via 1% and accept the two steps.

Someone invests 7% of their monthly salary, which is ₹2,170. They also invest 18% and 6%. Find the annual investment.

₹1,15,320. First 7% is ₹2,170, so the salary is ₹31,000. The total invested is 7 + 18 + 6 = 31%, which is ₹9,610 a month, and twelve times that is ₹1,15,320. Three steps, each of them this model.

When would these percentages NOT add?

Hard

A man spends 20% of his income on household expenditure. Of the remaining, he spends 30% on rent and 25% on travel, and saves the rest, which is ₹13,500. (a) Find his income. (b) Find what the answer would have been had all three percentages been of his income rather than of the remainder. (c) Explain which single word in the question decides between your two answers, and state a general rule for spotting it.

Follow-up

This puts the flat and nested readings side by side on one set of numbers, which is the sharpest way to see how much the reading is worth. Part (c) asks you to state the rule rather than apply it, and that is what makes it transfer to the next question.

Show the hint

For (a) the 30% and 25% are of the 80% that remains, so work out what fraction of the income survives all three deductions.