Home / Aptitude / Percentage / Successive Change or AB Method
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Q1. 
A dealer sells his goods to a retailer at a profit of 5% and the retailer sells it to a customer at a profit of 10%. By how much percentage is the customer’s price more than the dealer’s price? 
A. 16% 

B. 20% 

C. 15.5% 

D. 16.5% 
Apply AB Method.
5 + 10 + ^{5*10}/_{100} = 15.5
The customer’s price is 15.5% more than the dealer’s price.
Q2. 
A certain sum is invested at 10% p.a. for 2 years at compound interest. What will be the net percentage return on the sum invested? 
A. 21% 

B. 20.5% 

C. 22% 

D. 20% 
Compound interest is calculated on the amount.
Hence its is a case of successive change and we can apply AB Method.
10 + 10 + ^{10*10}/_{100} = 21
21% return on investment
Q3. 
Two successive discounts of 20 % and 25 % are equivalent to a single discount of what %? 
A. 45% 

B. 50% 

C. 40% 

D. 55% 
Apply AB Method.
 20  25 + ^{20*25}/_{100} = 40
40 indicates 40% discount
Q4. 
The value of an article is decreased by 10% and again decreased by 10%. What is the net effect on its price? 
A. 19% increase 

B. 29% decrease 

C. 20% decrease 

D. 19% decrease 
Apply AB Method.
 10  10 + ^{10*10}/_{100} = 19
19 indicates 19% decrease in the net price
Q5. 
The price of petrol is increased by 30% and then decreased by 20%. What is the net effect on its price? 
A. 4% decrease 

B. 4% increase 

C. 2% increase 

D. 6% increase 
Apply AB Method.
30  20  ^{30*20}/_{100} = 4
4% increase
Q6. 
The price of an article is increased by 20% and later it is decreased by 20%. Find the overall percentage change in the price? 
A. 4% increase 

B. No change 

C. 2% decrease 

D. 4% decrease 
Apply AB Method.
10  20  ^{20*20}/_{100} =  4
 4 indicates 4% decrease in the price
Q7. 
The salary of a worker first increase by 10% and later decrease by 10%. What is the net effect on his salary? 
A. No change 

B. 1% increase 

C. 1% decrease 

D. 0.1% decrease 
Apply AB Method.
10  10  ^{10*10}/_{100} =  1
1% decrease
Q8. 
The price of onion increases by 200% and therefore a family decreases its consumption by 50%. By how much percentage will the expenditure on onion change? 
A. 50% increase 

B. 100% increase 

C. 50% decrease 

D. 140% increase 
Apply AB Method.
200  50  ^{200*50}/_{100} = 50%
50% increase
Q9. 
The price of cooking oil increases by 60% and therefore a family decreases its consumption by 20%. By how much percentage will the expenditure on cooking oil change? 
A. 38% increase 

B. 28% decrease 

C. 18% increase 

D. 28% increase 
Apply AB Method.
60  20  ^{60*20}/_{100} = 28%
28% increase
Q10. 
The radius of a circle increases by 20%. By how much percentage will its area increase? 
A. 42% 

B. 44.4% 

C. 44% 

D. 44.2% 
Apply AB Method.
20 + 20 + ^{20*20}/_{100} = 44%
Q11. 
The side of a square increases by 10%. By how much percentage will its area increase? 
A. 20% 

B. 19% 

C. 22.1% 

D. 21% 
Apply AB Method.
10 + 10 + ^{10*10}/_{100} = 21%
Q12. 
The length of a rectangle increases by 20% and its breadth increases by 10%. By how much percentage will the area increase? 
A. 30% 

B. 32% 

C. 33% 

D. 31% 
Apply AB Method.
20 + 10 + ^{20*10}/_{100} = 32%
Q1. 
Three successive discounts of 10%, 20% and 30% are equivalent to a single discount of ? (a) 25% (b) 28% (c) 23% (d) 26% 
A. 46.9 % 

B. 48.6% 

C. 50.4% 

D. 49.6 % 
For three successive discounts, we need to apply the AB method twice.
 10 20 + ^{10*20}/_{100} =  28
 28  30+ ^{28*30}/_{100} =  49.6
 49.6 indicates 49.6 % discount
Q2. 
The length, breadth, and height of a cuboid increase by 20%, 10%, and 10% respectively. By how much% will the volume increase? 
A. 42% 

B. 45.2% 

C. 42.5% 

D. 60% 
Volume = l × b × h
There are 3 dimension, we need to apply AB method twice
20 + 10 + ^{20*10}/_{100} = 32
32 + 10 + ^{32*10}/_{100} = 45.2%
Hence the volume will increase by 45.2%
Q3. 
The price of petrol increases by 25%, a man reduces consumption by such a percent so that his expenditure can only go up by 15%. By what % does he decrease his consumption? 
A. 10% 

B. 8% 

C. 6.25% 

D. 5% 
Apply AB Method.
In this question decrease percentage consumption is asked. Let’s take it ‘x’
25 – x – ^{25*x} / _{100} = 15
– ^{5x}/_{4 }= – 10
X = ^{40}/_{5}
x = 8 %
Note: To solve these kinds of questions where either A or B (of AB method) is asked, you can use the hit and trial (Options elimination process) method to get the answer.
Ex. If we apply the first option i.e. 10%,
25  10  ^{25*10}/_{100} = 12.5% (net result must be 15. hence eliminated)
If we apply the second option i.e. 8%,
25  8  ^{25*8}/_{100} = 15% (net result must be 15. hence is the answer)
Q4. 
The price of petrol increases by 30%, a man reduces consumption by such a percent so that his expenditure can only go up by 10%. By what % does he decrease his consumption? 
A. 20% 

B. 17% 

C. 43% 

D. 15.38% 
Apply AB Method.
In this question decrease, the percentage of consumption is asked. Let’s take it ‘x’
30 – x – ^{30*x} / _{100} = 10
– ^{13x}/_{10 }= – 20
X = ^{200}/_{13}
x = 15.38 %
Note: To solve these kinds of questions where either A or B (of AB method) is asked, you can use the hit and trial (Options elimination process) method to get the answer.
Ex. If we apply the first option i.e. 20%,
30  20  30*20/100 = 4% (net result must be 10. hence eliminated)
Similarly, other options can be applied.
Q5. 
A shopkeeper marks his goods 50% above his cost price and allows a discount of 20%. What percentage profit does he make? 
A. 30% 

B. 20% 

C. 25% 

D. 15% 
It is a case of successive change.
Apply AB Method.
50  20  ^{50*20}/_{100} = 20
The shopkeeper makes a profit of 20%
Q1. 
The difference between compound interest and simple interest on a certain sum in 3 years at 10% p.a. is ₹ 155. Find the sum. 
A. ₹ 5000 

B. ₹ 4000 

C. ₹ 10000 

D. ₹ 1000 
General Method
$P{(1+\frac{10}{100})}^{3}P\frac{P\times 10\times 3}{100}=155$
After solving for P, we will get P = ₹ 5000
AB Method
SI = 10×3 = 30% ( In 1 year SI = 10%, In 3 years SI = 30%
CI = 33.1% (Applying AB method twice. $10+10+\frac{10\times 10}{100}=21$, $21+10+\frac{21\times 10}{100}=33.1\%$)
3.1% = 155
100% = ₹ 5000