- Case: Sugar Consumption Budget don’t change
- Case: Salary comparison: How much more or less?
- Case: Increased consumption absolute value
- Case: Apples price decrease absolute value
- Case: Time-Speed-Distance
- Mock questions
- Food for thought

**IF**you want to master this method, then don’t just read the article, simultaneously do all calculations in your rough-note/paper.

# Case: Sugar Consumption Budget don’t change

Q. if price of sugar is increased by 25%. But a family wants to keep its expenditure same as earlier. Then they should decrease their consumption by how much percentage?

- Suppose initial price of Sugar was Rs.100 per kg
- And this family needs 2 kg per month. (=quantity consumed)
- So what is their budget (or Expenditure?)

Before price rise | |

Price | 100 |

Quantity | 2 kg |

Budget = Price x quantity | 100 x 2=Rs.200 per month |

Now the price of sugar is increased by 25%.

So if previously it was Rs.100 per kg, now it is Rs.100+25=Rs.125 per kg.

Before | After | |

Price | 100 | 125 |

Quantity | 2 kg | |

Budget = Price x quantity | 100 x 2=Rs.200 per month |

If the family still wants to buy 2 kg sugar, they’ll have to pay Rs.125 x 2 = Rs.250. But they don’t want to increase their budget (Expenditure). Obviously they will have to cut down on their monthly consumption (Quantity of sugar.)

To solve this problem, just take ratio of both prices

100/125

=(25×4)/(25×5)

=4 / 5

It means 100/125=4/5

Now, reverse this ratio (4/5 =>5/4) and write it, in the table.

Means, in 100’s column, I’ll write 5 and in 125’s column, I’ll write 4.

Before | After | |

Price | 100 | 125 |

Ratio reversed? | 5 | 4 |

Demand | 2 kg | |

Budget = Price x Demand | 100 x 2=Rs.200 per month |

What is the percentage change in Ratio-Reversed?

Well, before it was “5” and after it has decreased to “4”.

% decrease from 5 to 4 is

=(5-4)/5

=1/5

=20% decrease.

That’s our answer.

If price is increased by 25% then we must decrease our consumption by 20% to keep the budget same.

Let’s check if our approach is correct.

According to above technique, we’ve found that consumption /demand should decrease by 20%.

So if earlier family consumed 2kg

Now they should consume only 100% minus 20%=80% of original demand

=80% of 2kg

=0.8 x 2

=1.6 kg

## Update the table.

Before | After | |

Price | 100 | 125 |

Quantity | 5 | 4 |

Budget = Price x quantity | 2 kg | 1.6 |

Price | 100 x 2=Rs.200 per month | 125 x 1.6=Rs.200 per month |

- As you can see, if we decrease demand/consumption from 2 kg to 1.6 then budget remains same (Rs.200).
- It proves that we’ve not made any mistake.

Another way is to use readymade formula

## Formula

Percentage decrease = 100m / (100+m), where m is the original percentage.

Therefore

Percentage decrease in sugar case

=100 x 25 / (100+25)

=100 x 25/125

=20% decrease.

- You can use whichever technique you like.
- But once you master product consistency, lot of profit-loss, time-speed-distance questions can be solved in less than a minute.
- Anyways, lets try some more “easy” questions and then move to difficult ones.

# Case: Salary comparison: How much more or less?

- If Salary of Mr.Abdul is 25% more then Mr.Bhide, then Mr.Bhide’s salary is how much % less than Mr.Abdul’s?

Assume Bhide earn Rs.100 per month Then Abdul has to earn Rs.100+25=125

Fill up the table.

Bhide | Abdul | |

Salary | 100 | 125 |

Ratio (reversed) |

Now get the ratio

100/125=4/5

Reverse it (from 4/5 to 5/4) and plug it in the table

Bhide | Abdul | |

Salary | 100 | 125 |

Ratio (reversed) | 5 | 4 |

That’s it. What is the decrease?

(5-4)/5 x 100

=1/5 x 100

=20% less

Final answer: Mr.Bhide’s salary is 20% less than Abdul’s.

Ofcourse you could directly calculate: (125-100)/125=20% but that won’t help us quickly solve the ‘complex’ cases situation like following.

# Case: Increased consumption absolute value

Q. A family spends Rs.600 on sugar every month. The price of sugar is decreased by 20% and they’re able to buy 5kg sugar more. What was the original price of sugar (per kg)?

- This is not at all complicated. Budget =Rs.600 (Constant)
- Assume that original price is Rs.100 (please note: this is not the answer, we are just ‘assuming).
- New price is 20% less = 100 minus 20 = Rs.80 per kg
- Assume that originally they used to buy “m” kilos of sugar every month.

Before | After | |

Price | Rs.100 | Rs.80 |

Ratio-reversed | ||

Quantity | M | |

Budget | 600 | 600 |

So if price is decreased by 20% then consumption quantity should increase by what percentage?

Just take ratio of price

100/80

=10/8

=5/4

Reverse It and fill up in the table

Before | After | |

Price | Rs.100 | Rs.80 |

Ratio-reversed | 4 | 5 |

Quantity | m | |

Budget |

So what’s the increase in quantity ?

Just look at the ratio reversed: 4 to 5. So increase is:

(5-4)/4 x 100

=1/4 x 100

=25%

- It means if sugar price decreases by 20% then we can buy 25% more sugar.
- So if earlier this family used to by “m” kilos of sugar, now they should be able to buy Total= (m + 25% of m) kilos of sugar.

How much more sugar can they buy? 25% of m

But the question itself says that family is able to buy 5 kg sugar more.

It means

25% of m =5 kg

(25/100) x m=5

M=5 x (100/25)

M=20kg

## Another way is (% to fraction)

25% when converted to fraction =1/4

So 1/4^{th} of m=5 kg

So m= 5 x 4=20 kg.

In either way: it means originally family used to buy 20 kilos of sugar.

And their budget was Rs.600. (given in the question)

So what was the per kilo price of sugar?

20kg=Rs.600

So 1 kg=600/20=30Rs. per kilo

Final answer= original price of sugar was Rs.30 per kg.

Let’s try a similar question, so our concept is crystal clear.

# Case: Apples price decrease absolute value

This is also from SSC-CGL exam.

Q. A man spends Rs.54 on apples every month. Price of Apple is decreased by 20% and this man can buy 10 apples more. What is the reduced price per dozen?

If price is 20% decreased => consumption should increased by 25% (as seen in previous case)

Suppose he used to buy “m” number of apples initially.

Now he can by 25% more apples.

But question itself says that he is buying 10 more apples.

Therefore,

25% of m =10

1/4 of m=10 (because 25%=25/100=1/4)

1/4 of m =10

M=40

## So what was the original price?

Total 54 rupees spent on 40 apples

=Rs.54/40

And we’ve to find answer in “dozen” so multiply with 12

Original price= Rs.(54/40) x 12

Donot simplify yet.

We’ve to find reduced price.

Question says, price is reduced by 20%.

So new price

=100 Minus 20=80%of original price

=0.8 x (54/40) x 12

=Rs.12.96

**Final answer:** the reduced price of apples is Rs.12.96 per dozen.

## Another approach

Originally he bought 40 apples.

Now he can buy 25% more

=100+25=125% of original apples

=1.25 x 40

=50 apples.

And his budget is Rs.54 means he buys 50 apples for 54 rupees,

50 apples | = 54 rupees |

12 apples | = how much? |

How much = 54 x 12 / 50 =Rs.12.96 per dozen.

Now let’s apply this concept in Time-Speed-Distance question

# Case: Time-Speed-Distance

Again from old SSC-CGL exam

Q. Walking at 6/7^{th} of his usual speed, a man is 25 minutes late for his destination.

What is his usual time to cover this distance (in hours)?

Speed x time = distance

This is same as price x quantity = budget.

Here distance remains the same, just like in “sugar-cases”, budget remains the same.

We don’t know his speed, so let’s assume his usual speed = 1 kmph

And his late speed = 6/7^{th} of usual speed = 6/7 x 1= 6/7 kmph

Usual case | Late case | |

Speed | 1 | 6/7 |

Ratio reversed |

Just take ratio

Usual/late=1/(6/7)=7/6

Reverse it (7/6 to 6/7 )and put it back in the table.

Usual case | Late case | |

Speed | 1 | 6/7 |

Ratio reversed | 6 | 7 |

Time | “T” |

Ok so if speed is decreased to 6/7^{th} then time is increased by what fraction (or percentage?)

6 to 7

=(7-6)/6

=1/6 increase in time.

Suppose his usual time was “T”, then it should be increased by 1/6^{th} of original time “T”

But we know that he is late by 25 minutes.

It means 1/6^{th} of T=25 minutes

1/6 x T = 25

T=25 x 6=150 minutes

But the question is asking time in hours.

150 minutes

=60 minutes + 60 minutes + 30 minutes

=1hour + 1 hour + 30 minutes

=2 hours and 30 minutes

Another way to convert minutes into hours

60 minutes = 1 hr

150 minutes = how many hours?

Therefore: How many hours = 1 x 150 / 60

When you divide 150 by “60” you 2 as quotient and 30 as remainder. So Correct answer is 2 hours and 30 minutes.

**Important:** In Minutes to hour conversion via division method, You should not cut zeros, else you get wrong answer.

For example, 150/60= 15/6 but when you divide 15 by 6, you get remainder 3 = answer comes as 2 hours and 3 minutes = wrong answer.

# Mock questions

- Journalist Popatlal’s income is 37.5% less than Dr. Iyyer’s. Then Dr.Iyyer’s income is how much % more than Popatlal’s income?
- If price of
-liquor is increased by 20% then Mohan should cut down consumption by what %, to keep his budget unchanged?*Desi* - Petrol price is doubled. But we don’t want to raise our expenditure. Then We should cut down our petrol consumption by what percentage?
- If the speed of a motorboat is decreased by one fourth, then journey completion time should increase by what percentage?
- Price of rice is increased from Rs. 6 to 7.5 per kg. If we don’t want to increase our Expenditure. We should decrease our rice-consumption by what percentage?
- Mobile company increased the call charges by 50%. If I want to keep my budget unchanged, I should reduce talk-time by what percentage?
- Dish TV has reduced the channel prices by 20% now I’m able to subscribe to 5 more channels in the same budget of Rs.400. How many channels did I subscribe earlier?
- Writing at 3/4
^{th}of my usual speed, I finished the question paper 20 minutes late. Had I written the answers at my regular speed, I could have finished the whole paper in how many hours? - Earlier UPSC used to ask 579 questions for 2900 marks. Now they want to decrease number of questions by 20% but want to keep total marks same as earlier. So, they should increase the marks per question by what percentage?
- If a politician’s bribe income is decreased by 10% then his anger increases by how much percentage? hahaha

## Answers

- Iyyer Popat
| 60% Perhaps this is the reason why Popat is unable to find a bride while Iyyer walked away with Babita-ji. |

- Desi liquor
| 16.67% decrease (1/6) |

- Petrol Double
| 50% decrease in consumption.(hint double = 100 to 200 =100% increase) |

- Motorboat
| One fourth=25% decrease=> 33.33% increase in time. |

- Rice
| 25% increase in price =>20% reduction in consumption. |

- Mobile talktime
| 50% increase in call rates=>33.33% decrease in talktime to keep budget unchanged. |

- Dish TV
| Earlier I had subscribed to 20 channels. 20% decrease in price= 25% increase in number of channels. so 1/4 of original channels=5, hence original number of channels=5 x 4 =20. |

- Writing speed
| 3/4 th of writing speed= reverse ratio is 4:3; and increase in time is 1/3 (=33.33%). So if 1/3 rd of original time= 20 minutes late. Then original time = 20 x 3 =60 minutes = 1 hour. |

- Anger
| 11.11% increase in anger lolz |

- UPSC
| Absolute values 579 and 2900 are irrelevant! No need to waste time in dividing them. 20% decrease=> increase marks per question by 25% percentage. |

# Food for thought

Try these two questions: (You can solve them via STD table method but try to solve them via this product consistency method. You’ll get the answer much more quickly!)

- Jethalal goes to shop at the speed 30 km/h, and he reaches six minutes early. Next day he goes at the speed of 24 km/h, and he reaches five minutes late. Find the distance between his home and shop. (
**Ans**=22kms) - Tappu walks from home to school @5kmph and reaches 15 minutes early. After the school is over, he is very tired. So he walks back from school to home at a slow speed of just 3kmph and reaches 9 minutes late. Find distance between his home and school. (
**Ans**=3 kms)

But How to apply “product consistency” ^here in these two question? =will be explained later.

All [Aptitude] Articles are listed at Mrunal.org/aptitude

## 83 Comments on “[Aptitude] Product Consistency: If Sugar price increases then consumption should be Decreased by What %, Time-Speed-Distance problems, shortcuts for SSC, IBPS, CSAT, CAT”

hey mrunal…can u help us out wid clocks and calendar probs….thnx!

sir can u provide us percentages problems .. As thr are many formulas in dis section to remember.. hoping dat u reduce d burden fr us by providin ur techniques to slove d probs ..

The time and speed problem in this article, if approached with your trademark STD method could solve without much hassle.

Thanks Mrunal

hello sir

pls help me with this quetn.

when the price of an article reduced by 20% its sale increased by 80%. what was the net effect on the sale?

Thanks Sir

Hi mrual,

i have been going thru STD shortcuts for timepdistance,avg,boat streams etc . In few places v use compenendo ,reverse ratio etc . i dont get the logic behind how to relate the question with this sub-techniques latter used in STD.

Thanks in advance.

very nice explaination

If the price of the rice increases by 25% then by what % should be the consumption be decreased so that the total expenditure is decreased by 10%?

a)35

b)26

c)28

d)25

answer with explanation…

Increase = 25% => 1/4 ==> new quantity = (1+4)/4= 5/4. Let the consumption be x. We want 10 percent decrease in our expenditure i.e 1/10==> therefore new exp = (10-1)/10= 9/10. Solve now: Quantity*consumption= expenditure ==> 5/4 *x = 9/10. ==> x=18/25. ==> decrease in consumption = from original 25 to new 18. i.e 7. Therefore, [7/25] *100= 28 % ANSWER. Hurray… !!

Sir

I am preparing for IBPS clerk exam and would like to have from you about how to prepare for it using less calculations.Hope to see your reply .

Thanks.

Shortcut for the ‘family-sugar’ type problems..

Sugar price decreased by 20% with which 5kg more sugar can be purchased

this means cost of 5kg sugar =120 (20% of 600)

so 1 kg sugar = 24(this is 20%decreased price)

orginal price=24/0.8 =30

Hope this helps

can i get any direct formula for this

thanksssssssssssssssssssss

If a man walks to his office at 5/4 of his usual rate he reaches office 30 min early than usual. What is his usual time to reach office.

Ans 5/2

Explain it

hiiiii , mrunal sir . can u plz help me to solve these two problems .

1) fresh fruit contains 68% of water & dry fruit contains 20% water . how much dry fruits can be obtained from 100 kg of fresh fruit.

2) if a liquid turned into solid , it’s volume increased by 10% .if solid is melted , the volume is reduced by how much percentage ?

Thank u mrunal ji.

superb!!!!!!!!!!!!!!!!!!!!!1

thanks a lot

hi,

very well xplained and this method is working for me.

but still i have bit confusion- why we interchange ratios?

though i undesrstand time and speed got inverse relation.

so guys please help with this.

thanks

please help me in solving this question:

After giving 25% discount on the entry ticket, the number of visitors increased by 30 %. What will be its impact in other days?

Kindly explain 10 number question UpSC one !! Didnt get how come 25% increases???please.

Q. Walking at 6/7th of his usual speed, a man is 25 minutes late for his destination.

What is his usual time to cover this distance (in hours).

Short trick: in these type of questions u can directly calculate like this 6*25/7-6=150 min means 2hrs 30 min.

time will be always in +ve, so make denominator positive by subtractor bigger number to smaller one.

its simple formula is (a/100-a) where ‘a’ is the 37.5% decrease of salary.

Hello sir /madam

can we solve following kind of ques by RR technique:

A has emplyed a worker for a certain work. He pays rs.20/- for each working day and payment is reduced by rs.3/- for each non working day of worker.

For how many worker remain absent from work if at the end of 120 days, worker gets rs.560/- as total remuneration?

kindly help. Thanks in advance

i made this equation for this question-

20d-3(120-d)=560 where d is the no of working days

solving this we get the answer as 80 days he did not work.

PRINTING MISTAKE =

9 IS 10

10 IS 9

sir, please say the detail answer of these question.

1)The price of an article first increased by 10%, then decreased by 20% and then increased by 30%. If the final price is Rs. 3432, what was the original price?

1.Rs. 2500

2.Rs. 3000

3.Rs. 2000

4.Rs. 3500

5.Rs. 1500

2)In how many ways 5 prizes can be distributed among 3 students if one student can get any number of prizes?

1.10

2.21

3.24

4.12

5.22

3) Four persons are there in a function and six seats are vacant. In how many ways they can be seated?

1.220

2.330

3.360

4.120

5.480

4)A bag contains six black balls, 4 green balls and 3 red balls. If 3 balls are picked at random what is the probability that they are of same colour?

1.25/286

2.25/216

3.42/72

4.3/13

5.4/13

1) 3000

2) 12

3) 360

4) 25/286

sir i am not finding percentage concept from starting..plzz send me a link

explain food for thought second question

Harish sold two chairs at Rs 600. In one he gain 20% & on the other he loses 20%. Find the gain & loss percent in whole transaction…..

…

400/100 i.e. 4% loss …. simlpy X to the power 2 divided by 100 always results in loss when selling price is same and % profit and loss is also same.

4% loss

Percentage decrease = 100m / (100+m), where m is the original percentage.

Therefore

Percentage decrease in sugar case

=100 x 25 / (100+25)

=100 x 25/125

=20% decrease.

How m=25 derive…! In here if m is original percentage then it must be100 not 25.. But it must be Inc. Or Dec. Value!! Please give some comment or guideline on this.

The price of sugar is increased by 28%. Therefore a family reduces its consumption so that the increment in the expenditure of sugar is only 20%. If the consumption of sugar is 15 kg before the increment, what is the consumption now?