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Discount & Successive Change

Mathematics · Commercial Arithmetic

Useful for: SSC CGL, Railway RRB, OSSC RHT — Regular High School Teacher, OSEPA Primary Teacher / JT Category-I, OSEPA Upper Primary — Science, OSSC Mathematics, OSSSC Govt Physical Education Teacher (PET), OSSSC Govt TGT Arts

and 4 more exams

OSSSC Govt TGT Science — CBZ, OSSSC Govt TGT Science — PCM, SSB Lecturer (Degree Colleges), SSB TGT PCM

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Overview

Two successive changes of a% and b% give a net change of a + b + ab/100; this one formula covers discounts, population and price-quantity problems.

Key points

Net change for successive a% and b%: a + b + ab/100.
A rise of r% followed by a fall of r% always gives a net loss of r²/100 %.
Successive discounts of d1% and d2% equal a single discount of d1 + d2 − d1d2/100.
Population after n years at r% growth: P(1 + r/100)^n.
Area change when length and breadth change by a% and b%: a + b + ab/100.

Explanation

For three changes, apply the formula twice.
Revenue = price × quantity: price up 20%, sales down 10% → 20 − 10 − 2 = +8%.
Depreciation: value after n years = V(1 − r/100)^n.
Order of successive changes does not matter for the net result.

Step by step

Write each change with its sign.
Apply a + b + ab/100.
Interpret positive as increase and negative as decrease.

Examples

+20% then −20%: 20 − 20 − 400/100 = −4% (net loss 4%).
Population 10,000 grows 10% a year for 2 years: 10,000 × 1.1 × 1.1 = 12,100.
Successive discounts of 20% and 10%: 20 + 10 − 2 = 28% single discount.

Traps and advanced points

Trap: Adding discounts directly (20% + 10% = 30% is wrong).
Trap: Forgetting the negative sign for a decrease in the formula.
Trap: Treating +r% then −r% as no change.

Quick revision

Net = a + b + ab/100.
Equal up and down → loss of r²/100 %.
Area/revenue are products → successive %.

Practice MCQs

A marked price of ₹1525 gets successive discounts of 10% and 10%. Find the final price.
1. 1159
2. 1387.75
3. 1311.5
4. 1235.25
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Answer: (d) 1235.25. Equivalent discount = 19%.
A marked price of ₹1800 gets successive discounts of 20% and 10%. Find the final price.
1. 1296
2. 1386
3. 1476
4. 1206
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Answer: (a) 1296. Equivalent discount = 28%.
A marked price of ₹2075 gets successive discounts of 15% and 20%. Find the final price.
1. 1307.25
2. 1514.75
3. 1618.5
4. 1411
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Answer: (d) 1411. Equivalent discount = 32%.
A marked price of ₹2350 gets successive discounts of 10% and 5%. Find the final price.
1. 1891.75
2. 2244.25
3. 2126.75
4. 2009.25
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Answer: (d) 2009.25. Equivalent discount = 14.5%.
A marked price of ₹2625 gets successive discounts of 20% and 5%. Find the final price.
1. 1995
2. 2126.25
3. 2257.5
4. 1863.75
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Answer: (a) 1995. Equivalent discount = 24%.
If A is 20% more than B and B is 25% less than C, then A is what percent of C?
1. 95%
2. 85%
3. 90%
4. 80%
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Answer: (c) 90%. Maano C=100.
A number is increased by 20% and then decreased by 20%. The net change is:
1. 4% increase
2. 2% decrease
3. 4% decrease
4. No change
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Answer: (c) 4% decrease. +20, -20 successive: 20-20-(20×20)/100 = -4%.
In an exam 35% failed in Maths, 45% in English, and 20% in both. The percentage who passed in both subjects is:
1. 35%
2. 25%
3. 40%
4. 30%
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Answer: (c) 40%. Failed in at least one = 35+45-20 = 60% (set union).
The price of an article is increased by 25%. To restore it to the original price, the new price must be decreased by:
1. 15%
2. 20%
3. 25%
4. 30%
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Answer: (b) 20%. 25/(100+25) × 100 = 25/125 × 100 = 20%.
If the numerator of a fraction is increased by 20% and denominator decreased by 10%, the fraction becomes 16/21. The original fraction is:
1. 2/3
2. 5/8
3. 4/7
4. 3/4
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Answer: (c) 4/7. Original = n/d.
Two candidates in an election; 10% voters did not vote. The winner got 55% of votes cast and won by 1800. Total voters on the list:
1. 25000
2. 20000
3. 18000
4. 22000
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Answer: (b) 20000. Votes cast = 90% of total = 0.9T.
A's income is 25% more than B's. B's income is what percent less than A's? (rounded)
1. 22%
2. 18%
3. 20%
4. 25%
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Answer: (c) 20%. 25/125 × 100 = 20%.
If 40% of (A+B) = 60% of (A-B), then A:B equals:
1. 4:1
2. 2:1
3. 5:1
4. 3:1
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Answer: (c) 5:1. 0.4(A+B) = 0.6(A-B) → 2(A+B) = 3(A-B) → 2A+2B = 3A-3B → 5B = A → A:B = 5:1.
The salary of a worker is first increased by 10% and then decreased by 5%. The net increase is:
1. 5.5%
2. 4%
3. 4.5%
4. 5%
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Answer: (c) 4.5%. Successive: 10 + (-5) + (10×-5)/100 = 5 - 0.5 = 4.5% increase.
In a mixture, milk and water are 60% and 40%. To make water 50%, per litre of mixture, water to be added (approx) is:
1. 0.2 L
2. 0.1 L
3. 0.25 L
4. 0.4 L
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Answer: (a) 0.2 L. 1 L mixture: milk 0.6, water 0.4.