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# Quickest way to solve problems based on successive discounts (Profit-Loss)

Feb 7, 2018 20:20 IST ssc reasoning preparation tips

The Quantitative Aptitude (QA) Section of government jobs exams like SSC includes many important topics from Arithmetic Ability. Some of them are Averages, percentages, simple interest & Compound interest, Profit & Loss, Discount, Ratio & proportion etc. Discount is one of the most important topics of Quantitatuive Aptitude section of these prsetigious examinations. This topic generally includes profit & loss related questions and are asked in almost all the competitive exams.But these questions invole logic as well as a lot of calculation.The only issue, thus in solving these type of questions  lies in the time that thy consume. And as we have to attempt a plenty of questions in the exam, it is not possible to devote such a long time on these discount based questions.In this post we will discuss about some easy and simple tips to solve these Discount based questions.So let us take first things first ie first we should know what actually Discount based questions are.

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What are Discount Based Questions?

Discount based comes under the Arithmetic ability topic of the Quantitative Aptitude Section and is a very important topic which, nowadays is frequently being asked in almost all the competitive exams. These types of questions are very simply framed and are a mere extension of Percentage calculation concept. They revolve around Profit & Loss, Selling Price & Marked Price.

Example: The marked price of a shirt is Rs.1000. A shopkeeper offers 10% discount on this shirt. How much will you have to pay, finally?

Solution:

• Discount =10% of 1000 = (10/100)*1000 =Rs 100
• Selling Price= 1000- 100 = Rs 900
• But in exam,you can do it directly in your head.So just thinkmthat 10 percent discount means you’ve to pay 100 percent minus 10 percent=90 percent of the marked price which means, (90/100)* 1000 =Rs. 900

What is marked price?

Marked price as the name suggests is the price of that is actually marked on the product. It is the same price on which you get discounts. Actually it is just a marketing propaganda to seduce customers. Suppose I am a seller and am running a store. I bought a Shirt for Rs.400, ie cost price for me is Rs 400. But I mark it and put a tag of Rs 1000 on it, which is now its marked price. Now, I give a huge dicount of 50% on iit, which means now it’s selling price will be 1000-5000 = Rs 500.Customer thinks I am giving a huge discount and might be making a loss in that deal, but in actual I am still making a profit of Rs 100.

What is Successive Discount?

It means discount on the discount. (Analogous to Compound Interest rate which signifies interest on interest)

Case 1: If there are two discounts:

The formula for total discount in case of successive-discounts:
If the first discount is x% and 2nd discount is y% then,

Total discount = ( x + y - xy /100)%

Example: The marked price of a shirt is Rs.1000. A shopkeeper offers 10% discount on this shirt and then again offers 20% discount on the new price. How much will you have to pay, finally?

Solution:

As the successive discount is 10% and 20%

Total discount = ( x + y - xy / 100 ) %

x = 10% and y = 20%

Total discount = [ 10 + 20 – ( 10 x 20) / 100] % = ( 30 – 200 /100 ) % = 28%

Discount = 28% of 1000 = ( 28 / 100 ) x 1000 = Rs 280

Selling price (SP)= Marked price (MP) – Discount = 1000-280 = Rs720

Case 1: If there are three discounts:

It means discount on the discount on the discount. (Analogous to Compound Interest rate which signifies interest on interest)

If there are three discounts as x%, y% and z% then find the total discount of x % and y% first and using it find the total discount with z%

Example: The marked price of a shirt is Rs.1000. A shopkeeper offers 10% discount on this shirt and then again offers 20% discount on the new price, and then and then again offers 30% discount on the new price . How much will you have to pay, finally?

Solution:

As the successive discount is 10% and 20% and then again 30%.Here we will move step by step and first calculate it for only two discounts, and then whatever the result comes, again calculating it fotr the result we got and the remaining discount.

Total discount = (x + y - xy / 100) %

• x = 10%, y = 20% and z = 30%
• Total discount = [10 + 20 – (10 x 20) / 100] % = (30 – 200 /100) % = 28% (let us say d)

Now, d= 28 % & z = 30 %

Total discount = (d + z - dz / 100) %

• Final discount = [28 + 30 – (28 x 30) / 100] % = (58 – 840 /100) % = 49.6%
• Which means Discount = 49.6% of 1000 = (49.6 / 100) x 1000 Rs 496
• Selling price = M.P – Discount = 1000- 496 = 504

Tips and Tricks to Solve Succesive Discount based Questions

The most important question is which discount is better among Successive discount and One Time Discount. So here by means of an example, we will explain the simple tricks to solve these Successive Discount baesed questuion quickly

Example: The marked price of a shirt is Rs.1000. A shopkeeper offers

Case 1: 10% discount on this shirt and then again offers 20% discount on the new price.

Case 2: 29 % discount

Which is the better deal?

Solution:

• Case 1: We have already solved case 1 & the net discount came out to be 28 % only, means Selling price = Rs 720
• Case 2: In case 2 we are getting Flat 29% discount which means, this deal is better for you as Selling price = Rs 710

But to arrive to this point we have to do a hell lot of calculation.What you can do is use shortcut technique

• Case 1: Successive discount 10% and then 20%, Final price you’ve to pay = 0.90 x 0.80 x original price = 0.72 x original price
• Case 2: Discount offered=29%, Final price you’ve to pay = 0.71 times original price, which is less than Case 1, means it is abetter deal.

This was all about tips and tricks to solve Succesive Discount based questions.So try the above tips and tricks on the questions based on Successive Discount.

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