1. Case: Sugar Consumption Budget don’t change
  2. Case: Salary comparison: How much more or less?
  3. Case: Increased consumption absolute value
  4. Case: Apples price decrease absolute value
  5. Case: Time-Speed-Distance
  6. Mock questions
  7. 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?

  1. 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 1/4th 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 6/7th of his usual speed, a man is 25 minutes late for his destination.
What is his usual time to cover this distance (in hours)?
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 = 6/7th 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 6/7th 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 1/6th of original time “T”
But we know that he is late by 25 minutes.
It means 1/6th 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

  1. 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?
  2. If price of Desi-liquor is increased by 20% then Mohan should cut down consumption by what %, to keep his budget unchanged?
  3. Petrol price is doubled. But we don’t want to raise our expenditure. Then We should cut down our petrol consumption by what percentage?
  4. If the speed of a motorboat is decreased by one fourth, then journey completion time should increase by what percentage?
  5. 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?
  6. Mobile company increased the call charges by 50%. If I want to keep my budget unchanged, I should reduce talk-time by what percentage?
  7. 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?
  8. Writing at 3/4th 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?
  9. 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?
  10. If a politician’s bribe income is decreased by 10% then his anger increases by how much percentage? hahaha

Answers

  1. Iyyer Popat
 60% Perhaps this is the reason why Popat is unable to find a bride while Iyyer walked away with Babita-ji.
  1. Desi liquor
 16.67% decrease (1/6)
  1. Petrol Double
 50% decrease in consumption.(hint double = 100 to 200 =100% increase)
  1. Motorboat
 One fourth=25% decrease=> 33.33% increase in time.
  1. Rice
 25% increase in price =>20% reduction in consumption.
  1. Mobile talktime
 50% increase in call rates=>33.33% decrease in talktime to keep budget unchanged.
  1. 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.
  1. 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.
  1. Anger
 11.11% increase in anger lolz
  1. 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!)

  1. 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)
  2. 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