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?

Logical 17 - Quantitative Reasoning

A, B, C and D are four friends living together in a flat and they have an agreement that whatever edible comes they will share equally among themselves. One day A’s uncle came to him and gave him a box of laddoos. Since no one was around, A divided the laddoos in four equal parts and ate his share after which he put the rest in the box. As he was closing the box, B walked in, took the Box from A & divided the ladoos in 4 equal parts & A & B took one part each and ate it. Suddenly C appeared and snatched the box. He again divided the laddoos in four equal parts, the three of them ate one part each and kept the remaining laddoos in the box. Later when D came he again divided the laddoos in four equal parts and all four ate their respective share. In total D ate 3 laddoos.

1. How many laddoos, in total did C eat?
(a) 12
(b) 15
(c) 39
(d) None of these

2. How many laddoos, in total did B eat?
(a) 24
(b) 15
(c) 39 
(d) None of these

3. How many laddoos, in total did A eat?
(a) 56
(b) 68
(c) 71 
(d) None of these

4. How many laddoos were given to A by his Uncle?
(a) 128
(b) 125
(c) 113
(d) None of these

5. How many laddoos did A eat the first time?
(a) 32 
(b) 24
(c) 15
(d) None of these


The following structure would work:

Hence, the answers are:
1. 3 + 12 = 15 (b)
2. 3 + 12 + 24 = 39 (c)
3. 3 + 12 + 28 + 32 = 71 (c)
4. 128 (a)
5. 32 (a)

Time to Think:

A man would like to take a new health insurance. An officer taking care of these matters says to the man, “Please tell me how many children you have.” The man answers, “I have three of them.” The officer, “What are the ages of your children?” The man answers, “The product of the ages is equal to 36.” The officer replies, “This is not enough information Sir!”; the man replied, “Sorry that I was a little bit unclear, but the sum of the ages is equal to the number of shops in front of your office.” The officer: “This still isn’t enough information Sir!”; The man replies, “My oldest child loves chocolate.” The officer: “Thanks for your cooperation, I now know the ages.” Are you as smart as the officer? Then give the sum of the ages of the children.

a. 13 
b. 22
c. 36 
d. 38

Verbal 9 - English Words of Foreign Origin

Italian Words

Prima dinna - principle female singer in an opera
Soprana - highest singing voice
Crescendo - gradual increase on volume or force
Bravo - well done
Quartet - group of four musicians
Maestro - famous conductor
Mandolin - stringed musical instrument
Finale - the last piece
Duet - a composition for two singers
Forte - to play loudly
Libretts - text of long musical piece
Allegro - at a quick and lively tempo
Presto - to be played very fast
Falsetto - high pitched singing method
Virtuoso - exceptional performer
Diva - women opera singer, famous lady
Dilettante - dabbler in art or knowledge
Bravura - great skill
Tempo - music's speed
Opera - musical drama
Piccolo - a very small flute - like musical instrument
Coda - final section of musical piece
Concerto - musical composition for soloist and orchestra
Madrigal - a song with parts
Balcony - a gallery
Villa - country, estate
Arcade - arched passageway, shops
Catacomb - tomb
mezzanine - lowest balcony
Portico - porch
Piozza - plaza
Grotto - cave
Corridor - hallway
Pedestal - a base or support
Alfresco - in the open air
Lotto - game of chance
Tarot - fortune telling cards
Valise - small piece of luggage
Garb - dress
Gondola - Venetian canal boat
Lagoon - area which is sand banked, saltwater lake
Gala - festive occasion, show
Casino - place for gambling
Cascade - waterfall, anything like a waterfall
Gazette - official newspaper for announcements
Incognito - assumed identity
Parasol - sunshade, umbrella
Regatta - meeting for yacht or boat races
Battalion - an army group
Fracas - uproar
Citadel - fortress
Bandit - robber
Salvo - a round of artillery
Vendetta - a private feud
Stiletto - a small dagger with a thin blade, a heel of female shoe
Cartel - alliance of political parties or business houses
Tirade - long angry speech
Partisan - prejudiced, adherent of a party, biased
Cavalcade - procession of riders, fleet of cars
Panache - dashing style
Manifesto - declaration of policy by a political party
Squadron - an army, navy or air force unit
Ducat - a gold coin
Mercantile - trade
Parmesan - cheese
Contra brand - smuggled goods
Porcelain - fine china, earthenware
Frigate - old warship, corresponding to modern cruiser
Skiff - small flat-bottomed boat
Milliner - maker or dealer in woman's hat
Settee - comfortable seat for two people
Bankrupt - financially insolvent


Yiddish Words

Schnapps - brandy, alcoholic drink
Challah - soft egg bread
Bagel - chewy roll with a hole in the middle
Matzoth - unleavened bread
Nosh - food, eat
Kosher - permitted, good (as of food)
Yenta - gossip
Boychik - little boy
Shmo - butt of a joke
Nudnick - bore
noodge - nag
Skiksa - non - jewish woman
Maven - expert
Klutz - clumsy person
Chai - life
Broche - blessing
Mazeltov - congratulations
Gesundneit - Good health
Chutzpah - boldness, self confidence
Bummer - annoying thing
Kvetch - to grumble or complain
Kibitzer - one who interferes
Golem - creature of clay brought to life by magic as in legend
Naches - proud pleasure
Mitzva - a good deed
Kine-abhora - Magical phrase to ward off evil
Fen - expression of disguist
Boo-boo - mistake
plotz - explode
Gehenna - hell
Mish-mosh - confusion
Bupkes - nothing
Mishegosa - nonsense
Phooeyl - expression of disguist, contempt

Answers Week 8

Logical 15 - Direction Test

Jack runs 10 m south from his flat, turns left and walks 23 m, again turns left and walks 40 m, then turns right and walks 5 m to reach his office. In which direction is the office from his house?

(a) East 

(b) Northeast

(c) Southwest 

(d) North

When we will look from F (Flat) to O (office) in the figure it can be observed that the direction is northeast. Option (b) is correct.

Quants 15 - Ratio and Proportion

The ratio between two numbers is 3 : 4 and their LCM is 180. The first number is:
The numbers would be 3x and 4x and their LCM would be 12x. 

12x = 180

x = 15; 3x = 45 and 4x = 60

This gives us the values as 45 and 60. The first number is 45.


Logical 16 - Direction Sense

Usain runs 100 m south from his house, turns left and runs 250 m, again turns left and runs 400m, then turns right and runs 50 m to reach to the stadium. In which direction is the stadium from his house?
(a) Southwest 
(b) Northeast
(c) East 
(d) North

The stadium is northeast with respect to the house. Option (b) is correct.


Quants 16 - Ratio and Proportion

If 30 men working 7 hours a day can do a piece of work in 18 days, in how many days will 21 men working 8 hours a day do the same work?

The total number of manhours required = 30 × 7 × 18 = 3780

21 × 8 × no. of days Æ 3780/168 = 22.5 days.

Quants 16 - Ratio and Proportion

Practice Questions:

Question 1:

The students in three batches at Mindworkzz are in the ratio 2 : 3 : 5. If 20 students are increased in each batch, the ratio changes to 4 : 5 : 7. The total number of students in the three batches before the increases were

2x + 20 : 3x + 20 : 5x + 20 = 4 : 5 : 7 Æ x = 10 and initially the number of students would be 20, 30 and 50 Æ a total of 100.

Question 2:

The speeds of three cars are in the ratio 2 : 3 : 4. The ratio between the times taken by these cars to travel the same distance is

The ratio of time would be such that speed × time would be constant for all three. Thus if you take the speeds as 2x, 3x and 4x respectively, the times would be 6y, 4y and 3y respectively. (LCM of 2, 3, 4 is 12 and so (2 x 6; 3 x 4; 4 x 3).

Question 3:

` 2250 is divided among three friends Amar, Bijoy and Chandra in such a way that 1/6th of Amar’s share, 1/4th of Bijoy’s share and 2/5th of Chandra’s share are equal. Find Amar’s share.

(a) ` 720 

(b) ` 1080

(c) ` 450 

(d) ` 1240

Amar’s share should be divisible by 6. Option d gets rejected by this logic.

Further: A + B + C = 2250. If Amar’s share is 720 (acc. To option a) Bijoy’s share should be 480 & Chandra’s share should be 300. (Gives us a total of 720 + 480 + 300 = 1500).

But the required total is 2250 (50% more than 1500). Since all relationships are linear, 1500 will increase to 2250 if we increase all values by 50%. Hence, Amar’s share should be 1080.

Question 4:

If 30 oxen can plough 1/7th of a field in 2 days, how many days 18 oxen will take to do the remaining work?

60 oxen days = 1/7 of the field Æ 420 oxen days are required to plough the field. Thus, the remaining work would be 360 oxen days. With 18 oxen, it would take 20 days.

Question 5:

A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?

Assume that 1 cat leap is equal to 3 metres and 1 dog leap is equal to 4 metres.
Then the speed of the cat in one unit time = 3 × 5 = 15 meters.
Also, the speed of the dog in one unit time = 4 × 4 = 16 meters.
The required ratio is 15:16

Time to Think:

If 30 men working 7 hours a day can do a piece of work in 18 days, in how many days will 21 men working 8 hours a day do the same work?

Logical 16 - Direction Sense

Practice Questions:

Question 1:

Two cars start from the opposite points of straight part of the National Highway 8, 100 km apart. The first car runs for 20 km. It then takes a detour—takes a right turn goes straight for 15 km. It then turns left, runs for another 25 km and then takes the straight connecting road to reach back on the main road. In the meantime, due to a minor breakdown, the other car has run only 35 km along the main road. What would be the distance between the two cars at this point?

(a) 20 km 
(b) 30 km
(c) 45 km 
(d) 10 km

From the above figure it is clear that Car 1 would move 45 kms along the highway while Car 2 would run 35 kms along the same highway. Naturally, the distance between the two cars at this time would be 20 km. Option (a) is correct.

Question 2:

A messenger was returning to his base station which was in front of him to the north. When his base station was 100 m away from him, he turned to the left and moved 50 m to deliver the last message to the Peshwa’s troops. He then moved in the same direction for 40 m, turned to his right and moved 100m. How many meters away he was now from his base station?

(a) 0 
(b) 150
(c) 90 
(d) 100

Option (c) is correct.


Question 3:

A watch in Huckleberry Finn’s house reads 4·30. If the minute hand points towards the West, in which direction does the hour hand point?

(a) Northeast 
(b) Southwest
(c) Northwest
 (d) North

If minute hand is pointing towards west, there will be a difference of 45 degrees in the minute hand and the hour hand at 4:30. And that difference would be in the anticlockwise direction. So, southwest.
Option (a) is correct.

Question 4:

Raveena walks 10 km south from her house, turns left and walks 25 km, again turns left and walks 40 km, then turns right and walks 5 km to reach her office. In which direction was the office from her house?

(a) Southwest 

(b) Northeast

(c) East 

(d) North

The journey would be as per the figure. Her office would be northeast from her house.
Option (b) is correct.

Question 5:

Hanuman, while looking for the Sanjeevani booty travels 3 km to the west, turns left and goes 3 km, turns right and goes 1 km, again turns right and goes 3 km. How far is he from the starting point?

(a) 7 km

(b) 6 km

(c) 5 km 

(d) 4 km

From the figure it is evident that the distance is 4 kms. Option (d) is correct.

Time to Think:

Usain runs 100 m south from his house, turns left and runs 250 m, again turns left and runs 400m, then turns right and runs 50 m to reach to the stadium. In which direction is the stadium from his house?

(a) Southwest 

(b) Northeast

(c) East 

(d) North