mrunal [aptitude] product consistency_ if sugar price increases then consumption should be decreased...

[Aptitude] Product Consistency: If Sugar price increases then consumptionshould be Decreased by What %, Time-Speed-Distance problems, shortcuts forSSC, IBPS, CSAT, CAT

Case: Sugar Consumption Budget dont change1.Case: Salary comparison: How much more or less?2.Case: Increased consumption absolute value3.Case: Apples price decrease absolute value4.Case: Time-Speed-Distance5.Mock questions6.Food for thought7.

IF you want to master this method, then dont just read the article, simultaneously doall calculations in your rough-note/paper.

Case: Sugar Consumption Budget dont change

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

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

Before price risePrice 100Quantity 2 kgBudget = 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 AfterPrice 100 125Quantity 2 kgBudget = Price x quantity 100 x 2=Rs.200 per month

If the family still wants to buy 2 kg sugar, theyll have to pay Rs.125 x 2 = Rs.250. Butthey dont want to increase their budget (Expenditure). Obviously they will have to cutdown on their monthly consumption (Quantity of sugar.)

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1 of 8 7/28/2014 10:24 AM

To solve this problem, just take ratio of both prices100/125=(254)/(255)=4 / 5It means 100/125=4/5Now, reverse this ratio (4/5 =>5/4) and write it, in the table.Means, in 100s column, Ill write 5 and in 125s column, Ill write 4.

Before AfterPrice 100 125Ratio reversed? 5 4Demand 2 kgBudget = 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.Thats our answer.If price is increased by 25% then we must decrease our consumption by 20% to keepthe budget same.Lets check if our approach is correct.According to above technique, weve found that consumption /demand should decreaseby 20%.So if earlier family consumed 2kgNow 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 AfterPrice 100 125Quantity 5 4Budget = Price x quantity 2 kg 1.6Price 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 budgetremains same (Rs.200).It proves that weve not made any mistake.

Another way is to use readymade formula

Formula


2 of 8 7/28/2014 10:24 AM

Percentage decrease = 100m / (100+m), where m is the original percentage.ThereforePercentage 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-distancequestions 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.Bhides salary is howmuch % less than Mr.Abduls?

1.

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

Bhide AbdulSalary 100 125Ratio (reversed)

Now get the ratio100/125=4/5Reverse it (from 4/5 to 5/4) and plug it in the table

Bhide AbdulSalary 100 125Ratio (reversed) 5 4

Thats it. What is the decrease?(5-4)/5 x 100=1/5 x 100=20% lessFinal answer: Mr.Bhides salary is 20% less than Abduls.Ofcourse you could directly calculate: (125-100)/125=20% but that wont help usquickly 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 by20% and theyre able to buy 5kg sugar more. What was the original price of sugar (perkg)?

This is not at all complicated. Budget =Rs.600 (Constant)


3 of 8 7/28/2014 10:24 AM

Assume that original price is Rs.100 (please note: this is not the answer, we arejust assuming).New price is 20% less = 100 minus 20 = Rs.80 per kgAssume that originally they used to buy m kilos of sugar every month.

Before AfterPrice Rs.100 Rs.80Ratio-reversedQuantity MBudget 600 600

So if price is decreased by 20% then consumption quantity should increase by whatpercentage?Just take ratio of price100/80=10/8=5/4Reverse It and fill up in the table

Before AfterPrice Rs.100 Rs.80Ratio-reversed 4 5Quantity mBudget

So whats 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 tobuy Total= (m + 25% of m) kilos of sugar.

How much more sugar can they buy? 25% of mBut the question itself says that family is able to buy 5 kg sugar more.It means25% of m =5 kg(25/100) x m=5M=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


4 of 8 7/28/2014 10:24 AM

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.600So 1 kg=600/20=30Rs. per kiloFinal answer= original price of sugar was Rs.30 per kg.Lets 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 inprevious 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 =101/4 of m=10 (because 25%=25/100=1/4)1/4 of m =10M=40

So what was the original price?

Total 54 rupees spent on 40 apples=Rs.54/40And weve to find answer in dozen so multiply with 12Original price= Rs.(54/40) x 12Donot simplify yet.Weve 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.12.96Final 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,


5 of 8 7/28/2014 10:24 AM

50 apples = 54 rupees12 apples = how much?

How much = 54 x 12 / 50 =Rs.12.96 per dozen.Now lets 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 = distanceThis is same as price x quantity = budget.Here distance remains the same, just like in sugar-cases, budget remains the same.We dont know his speed, so lets 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 caseSpeed 1 6/7Ratio reversed

Just take ratioUsual/late=1/(6/7)=7/6Reverse it (7/6 to 6/7 )and put it back in the table.

Usual case Late caseSpeed 1 6/7Ratio reversed 6 7Time T

Ok so if speed is decreased to 6/7th then time is increased by what fraction (orpercentage?)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 timeTBut we know that he is late by 25 minutes.

It means 1/6th of T=25 minutes1/6 x T = 25T=25 x 6=150 minutesBut 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


6 of 8 7/28/2014 10:24 AM

Another way to convert minutes into hours60 minutes = 1 hr150 minutes = how many hours?Therefore: How many hours = 1 x 150 / 60When you divide 150 by 60 you 2 as quotient and 30 as remainder. So Correctanswer is 2 hours and 30 minutes.Important: In Minutes to hour conversion via division method, You should not cutzeros, else you get wrong answer.For example, 150/60= 15/6 but when you divide 15 by 6, you get remainder 3 = answercomes as 2 hours and 3 minutes = wrong answer.

Mock questions

Journalist Popatlals income is 37.5% less than Dr. Iyyers. Then Dr.Iyyersincome is how much % more than Popatlals income?

1.

If price of Desi-liquor is increased by 20% then Mohan should cut downconsumption by what %, to keep his budget unchanged?

2.

Petrol price is doubled. But we dont want to raise our expenditure. Then Weshould cut down our petrol consumption by what percentage?

3.

If the speed of a motorboat is decreased by one fourth, then journey completiontime should increase by what percentage?

4.

Price of rice is increased from Rs. 6 to 7.5 per kg. If we dont want to increaseour Expenditure. We should decrease our rice-consumption by what percentage?

5.

Mobile company increased the call charges by 50%. If I want to keep my budgetunchanged, I should reduce talk-time by what percentage?

6.

Dish TV has reduced the channel prices by 20% now Im able to subscribe to 5more channels in the same budget of Rs.400. How many channels did I subscribeearlier?

7.

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 wholepaper in how many hours?

8.

Earlier UPSC used to ask 579 questions for 2900 marks. Now they want todecrease number of questions by 20% but want to keep total marks same asearlier. So, they should increase the marks per question by what percentage?

9.

If a politicians bribe income is decreased by 10% then his anger increases byhow much percentage? hahaha

10.

Answers

Iyyer Popat1.60% Perhaps this is the reason why Popat is unable to find a bridewhile Iyyer walked away with Babita-ji.

Desi liquor2. 16.67% decrease (1/6)

PetrolDouble

3. 50% decrease in consumption.(hint double = 100 to 200 =100%increase)


7 of 8 7/28/2014 10:24 AM

Food for thought

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

Jethalal goes to shop at the speed 30 km/h, and he reaches six minutes early. Nextday he goes at the speed of 24 km/h, and he reaches five minutes late. Find thedistance between his home and shop. (Ans=22kms)

1.

Tappu walks from home to school @5kmph and reaches 15 minutes early. Afterthe school is over, he is very tired. So he walks back from school to home at aslow speed of just 3kmph and reaches 9 minutes late. Find distance between hishome and school. (Ans=3 kms)

2.

But How to apply product consistency ^here in these two question? =will beexplained later.All [Aptitude] Articles are listed at Mrunal.org/aptitude

URL to article: http://mrunal.org/2013/01/aptitude-product-consistency-shortcuts-ssc-ibps-csat-cat.html

Posted By Mrunal On 17/01/2013 @ 19:37 In the category Aptitude


8 of 8 7/28/2014 10:24 AM

mrunal [aptitude] product consistency_ if sugar price increases then consumption should be decreased...

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