Quants 18 - Profit and Loss

Practice Questions:

Question 1:

By selling a watch for ` 495, a shopkeeper incurs a loss of 10%. Find the cost price of the watch for the shopkeeper.

Selling Price = 495

Loss = 10%

Cost Price = ?

0.9 × CP = 495 

CP = 495 / 0.9 = 495 / (9/10) = 495 * 10 / 9 = 550.

Question 2:

By selling a cap for ` 34.40, a man gains 7.5%. What will be the CP of the cap?

Selling Price = 34.40

Gain = 7.5%

Cost Price = ?

The SP = 107.5% of the CP. Thus, CP = 34.4/1.075 = 32.

Question 3:

A machine costs ` 375. If it is sold at a loss of 20%, what will be its cost price as a percentage of its selling price?

A loss of 20% means a cost price of 100 corresponding to a selling price of 80. CP as a percentage of the SP would then be 125%

Question 4:

A shopkeeper sold goods for ` 2400 and made a profit of 25% in the process. Find his profit per cent if he had sold his goods for ` 2040.

2400 = 1.25 × cost price Æ Cost price = 1920

Profit at 2040 = ` 120

Percentage profit = (120/2040) × 100 = 6.25%

Question 5:

A digital diary is sold for ` 935 at a profit of 10%. What would have been the actual profit or loss on it, if it had been sold for ` 810?

CP = 935/1.1 = 850. Selling this at 810 would mean a loss of `40 on a CP of ` 850.

Time to Think:

A cellular phone when sold for ` 4600 fetches a profit of 15%. Find the cost price of the cellular phone.

Quants 17 - Percentage

Key Points to Remember:

Whenever the value of a measured quantity changes, the change can be captured through

(a)Absolute value change or

(b)Percentage change.

Both these measurements have their own advantages and disadvantages.

Absolute value change: It is the actual change in the measured quantity. For instance, if sales in year 1 is ` 2500 crore and the sales in year 2 is ` 2600 crore, then the absolute value of the change is ` 100 crore.

Percentage change: It is the percentage change got by the formula

Percentage change = Absolute Value Change / Original Quantity × 100

= 100 / 2500 × 100 = 4%

As seen earlier, this often gives us a better picture of the effect of the change.

Practice Questions:

Question 1:
The population of a city grew from 20 lakh to 22 lakh. Find the
(a) percentage change
(b) percentage change based on the final value of population

(a) percentage change = (2/20) × 100 = 10%

(b) percentage change on the final value = (2/22) × 100 = 9.09%

Question 2:

Due to a 25% price hike in the price of rice, a person is able to purchase 20 kg less of rice for ` 400. Find the initial price.

Since price is rising by 25%, consumption has to decrease by 20%. But there is an actual reduction in the consumption by 20 kg. Thus, 20% decrease in consumption is equal to a 20 kg drop in consumption.

Hence, original consumption is: 100 kg of rice.

Money spent being ` 400, the original price of rice is ` 4 per kg.

Question 3:

The cost of manufacture of an article is made up of four components A, B, C and D which have a ratio of 3 : 4 : 5 : 6 respectively. If there are respective changes in the cost of +10%, –20%, –30% and +40%, then what would be the percentage change in the cost.

Assume the cost components to be valued at 30, 40, 50 and 60 as you read the question. Then we can get changed costs by effecting the appropriate changes in each of the four components. Thus we get the new cost as 33, 32, 35 and 84 respectively. The original total cost was 180 the new one is 184. The percent change is 4/180 = 2.22%.

Question 4:

In an election between 2 candidates, Bhiku gets 65% of the total valid votes. If the total votes were 6000, what is the number of valid votes that the other candidate Mhatre gets if 25% of the total votes were declared invalid?

Total votes = 6000. Valid votes = 75% of 6000 = 4500. Bhiku gets 65% of 4500 votes and Mhatre gets 35% of 4500. Hence, Mhatre gets: 0.35 × 4500 = 1575 votes.

Question 5:

Arjit Sharma generally wears his father’s coat. Unfortunately, his cousin Shaurya poked him one day that he was wearing a coat of length more than his height by 15%. If the length of Arjit’s father’s coat is 120 cm then find the actual length of his coat.

Let Arjit’s height be H. Then, H × 1.15 = 120 Æ H = 120/1.15 = 104.34.

Time to Think:

Ram sells his goods 25% cheaper than Shyam and 25% dearer than Bram. How much percentage is Bram’s goods cheaper than Shyam’s?