Quants 26 - Interests

 Practice Questions:

Question 1:

What is the difference between the simple interest on a principal of ` 500 being calculated at 5% per annum for 3 years and 4% per annum for 4 years?

5% for 3 years (SI) = 15% of the amount; At the same time 4% SI for 4 years means 16% of the amount. The difference between the two is 1% of the amount. 1% of 500 = ` 5

(or)

SI = PNR/100 = (500*5*3)/100 = 75

SI = PNR/100 = (500*4*4)/100 = 80

Difference = 80 - 75 = 5.

Question 2:

In what time will ` 3300 become ` 3399 at 6% per annum interest compounded half-yearly?

Since compounding is half yearly, it is clear that the rate of interest charged for 6 months would be 3% 

3300 -3%- 3399.

Question 3:

What is the simple interest for 9 years on a sum of ` 800 if the rate of interest for the first 4 years is 8% per annum and for the last 4 years is 6% per annum?

8% of 800 for 4 years + 6% of 800 for 4 years = 64 × 4 + 48 × 4 = 256 + 192 = 448. 

However, we do not know the rate of interest applicable in the 5th year and hence cannot determine the exact simple interest for 9 years.

Question 4:

What is the difference between compound interest and simple interest for the sum of ` 20,000 over a 2 year period if the compound interest is calculated at 20% and simple interest is calculated at 23%?

Simple interest @ 23% = 4600 × 2 = 9200
Compound interest @ 20%

20000 -20%- 24000 -20%- 28800 Æ ` 8800 compound interest.
Difference = 9200 – 8800 = ` 400.

Question 5:

Find the compound interest on ` 1000 at the rate of 20% per annum for 18 months when interest is compounded half-yearly.

1000 -10%- 1100 -10%- 1210 -10%- 1331.
Compound interest = 1331 – 1000 = ` 331

Time to Think:

What is the simple interest on a sum of `700 if the rate of interest for the first 3 years is 8% per annum and for the last 2 years is 7.5% per annum?

Quants 25 - Interest

Practice Questions:

Question 1:

` 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

The annual interest would be ` 60 (PNR/100 = (1200*1*5)/100). 

After 3 years the total value would be 1200 + 60 × 3 = 1380.

Question 2:

Interest obtained on a sum of ` 5000 for 3 years is ` 1500. Find the rate percent.

The interest earned per year would be 1500/3=500. This represents a 10% rate of interest.

SI = PNR/100 => 1500 = (5000 x 3 x R)/100 => R = 1500 x 100 / ( 5000 x 3 ) = 10%.

Question 3:

` 2100 is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.

2100 + 5% of 2100 = 2100 + 105 = 2205 (after 1 year). 

Next year it would become:
2205 + 5% of 2205 = 2205 +110.25 = 2315.25

Question 4:

Find the difference between the simple and the compound interest at 5% per annum for 2 years on a principal of ` 2000.

Simple Interest for 2 years = 100 + 100 = 200.
Compound interest for 2 years: 

Year 1 = 5% of 2000 = 100.
Year 2: 5% of 2100 = 105 Æ Total compound interest = ` 205.
Difference between the Simple and Compound interest = 205 – 200 = ` 5

Question 5:

After how many years will a sum of ` 12,500 become ` 17,500 at the rate of 10% per annum?

12500 @ 10% simple interest would give an interest of ` 1250 per annum. For a total interest of ` 5000, it would take 4 years.

Time to Think:

Find the rate of interest if the amount after 2 years of simple interest on a capital of ` 1200 is ` 1440.

This week and the following week is a special week for Quantitative aptitude. Full fledged to concepts in 10 days!! Happy learning!!

Answers Week 12

Quants 23 - Stocks and Shares

A 9% stock yields 8%. The market value of the stock is:

To obtain Rs.8, investment, Rs. 100

To obtain Rs.9, investment, Rs. (100/8) * 9 = Rs.112.50

Market value of Rs. 100 stock = Rs.112.50

 

Logical 23 - Classification

a) Pistol

b) Sword

c) Gun

d) Rifle

e) Cannon

Here, all except Sword are fire arms, and can be used from a distance.

a) Cathedral

b) Mosque

c) Church

d) Monastery

e) Temple

All except Monastery are places of worship, while monastery is a place where monks stay.


Verbal 12 - Sentence Completion

We have to bear our own burdens.

Napoleon was killed in the battle of Waterloo.

The world is on the verge of a third world war.

Barter is an economic transaction involving exchange of articles.

The premises is for sale.

Logical 24 - Verification of Truth of the Statement

A factory always has

a) Electricity

b) Chimney

c) Workers

d) Files

e) Sellers

A clock always has

a) Battery

b) Numbers

c) Alarm

d) Needles

e) Frame


Quants 23 - Stocks and Shares

A can do a work in 15 days and B in 20 days. If they work together for 4 days, then the fraction of the work left is:

A's 1 day work = 1/15

B's 1 day work = 1/20
A+B's 1 day work = 1/15 + 1/20 = 7/60
A+B's 4 days work = 7/60 * 4 = 7/15
Thus, remaining work = 1 - 7/15 = 8/15

Quants 24 - Time and Work

Practice Questions:

Question 1:

Sakshi can do a piece of work in 20 days. Ziva is 25% more efficient than Sakshi. The number of days taken by Ziva to do the same piece of work is:

Ratio of times taken by Sakshi and Ziva is 125:100 = 5:4
Suppose Ziva takes x days to do the work,
5 : 4 :: 20 : x => x = (4 * 20) / 5 = 80/5 = 16 days.
Hence, Ziva takes 16 days to complete the work.

Question 2:

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could do in 23 days?

Ratio of times taken by A and B = 100:130 = 10:13
Suppose B takes x days to do the work,
Then 10 : 13 :: 23 : x => x = (23 * 13) / 10 = 299/10
A's 1 day work = 1/23; B's 1 day work = 10/299
A+B 's 1 day work = 1/23 + 10/299 = 23/299 = 1/13
A and B together can complete the work in 13 days.

Question3:

A does half as much as B in three-fourth of the time. If together, they take 18 days to complete the work, how much time shall B take to do it?

Suppose B takes x days to complete the work,
A takes 2*(3/4)x = 3/2 x days
A+B 's 1 day work = 1/18
1/x + 2/3x = 1/18
x = 36/5 days.

Question 4:

A is 50% as efficient as B. C does half of the work done by A and B together. If C alone does the work in 40 days, then A, B and C together can do the work in:

A's 1 day work : B's 1 days work = 150 : 100 = 3 : 2
Let A's and B's 1 day work be 3x and 2x respectively.
Then C's 1 day work = (3x+2x)/2 = 5x/2
5x/2 = 1/40 => 5x = 1/20 => 100x = 1
x= 1/100
A's 1 day work = 3/100
B's 1 day work = 2/100 = 1/50
C's 1 day work = 5/100 / 2 = 5/200 = 1/40
A+B+C 's 1 day work = 3/100 + 2/100 + 5/200 = 15/200 = 3/40
So, A, B and C can complete the work in 40/3 = 13 1/3 days.

Question 5:

Two workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:

Let A's 1 day work = x
Let B's 1 day work = y
Then x+y = 1/5 and 2x + 1/3y = 1/3
Solving the above 2 equations,
x = 4/25 and y = 1/25
A's 1 day work = 4/25
So, A alone could complete the work in 25/4 = 6 1/4 days.

Time to Think:

A can do a work in 15 days and B in 20 days. If they work together for 4 days, then the fraction of the work left is:

Logical 24 - Verification of Truth of the Statement

Key Points to Remember:

In this type of questions, we are required to stress only on the truth of the facts that always hold. Questions are asked in context of a particular thing or factor that is always characterized by a specific part or feature. The alternatives other than the correct answer also seem to bear a strong relationship with the thing mentioned. So, the absolute truth is to be followed. 

Examples:

1. Atmosphere always has

a) Oxygen

b) Air

c) Germs

d) Moisture

e) Dust

Clearly, though all the alternatives may form a part of the atmosphere, the air is the most vital part, without which there can be no atmosphere. 

2. A train always has

a) Engine

b) Rails

c) Driver

d) Guard

e) Passengers

Clearly, rails are necessary for the train to move on. Driver alone can move the train. A guard is also necessary for safety. A train is moved for the passengers. But all these do not constitute a train. A train cannot be called so without the engine. 

3. Which one of the following is always found in Bravery?

a) Courage

b) Experience

c) Power

d) Knowledge

Clearly, bravery is a quality exhibited only by a person who possesses courage. 

Practice Questions:

4. Which of the following an animal always has?

a) Lungs

b) Skin

c) Mind

d) Heart

e) Life

5. A race always has

a) Referee

b) Spectators

c) Rivals

d) Prize

e) Victory

6. Which of the following a Drama must have?

a) Actors

b) Story

c) Sets

d) Director

e) Spectators

7. A book always has

a) Chapters

b) Pages

c) Contents

d) Pictures

e) Illustrations

8. A mirror always

a) Reflects

b) Retracts

c) Distorts

d) Refracts

e) Reveals the truth

Time to Think

9. A factory always has

a) Electricity

b) Chimney

c) Workers

d) Files

e) Sellers

10. A clock always has

a) Battery

b) Numbers

c) Alarm

d) Needles

e) Frame

Verbal 12 - Sentence Completion

Fill in the blanks with the appropriate words from the options given below. Do not use the same word twice. 

[ abolished, abated, abdicated, abandoned, able, rebates, capable, abridged, banished, capacious, abbreviation, about, bear, exile, bared, sale, war, barter, battle, above ]

Practice Questions:

1. Lord Buddha abdicated his kingship and became a hermit.

2. The Indian Government abolished slavery.

3. The residents abandoned the haunted house.

4. The rain abated after some time.

5. The shops offer rebates in the off season.

6. Our government is able to confront any type of situation.

7. He is capable of solving this problem.

8. Confucius possessed a capacious mind.  

9. B.A. is an abbeviation  of "Bachelor of Arts".

10. Abridged versions of classics are easier to read than the original versions.
11.  It was about ten in the night when we reached home.

12. The painting was hung above the window.

13. The Shah of Iraq was banished from his country.

14. Prospero, a character of Shakespeare's play "The Tempest" was living in exile.

15. The patient bared his chest when the Doctor examined him.

Time to Think:

 

16. We have to _______ our own burdens.

17. Napoleon was killed in the _______ of Waterloo.

18. The world is on the verge of a third world _______.

19. _______ is an economic transaction involving exchange of articles.

20. The premises is for _______.