1. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:

A.20 days B.221days

2C.25 days D.30 days

Answer: Option B

Explanation:

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes3

x 60 = 90 days.2

So, A takes 30 days to do the work.

A's 1 day's work =1

30

B's 1 day's work =190

(A + B)'s 1 day's work =

1

+

1

=

4

=

2

30 90 90 45

A and B together can do the work in 45

= 221

days.

2 2

2. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?A.3 : 4 B.4 : 3C.5 : 3 D.Data inadequate

Answer: Option B

Explanation:

(20 x 16) women can complete the work in 1 day.

1 woman's 1 day's work =1

.320

(16 x 15) men can complete the work in 1 day.

1 man's 1 day's work =1

240

So, required ratio =1

:1

240 320

=1

:1

3 4= 4 : 3 (cross multiplied)

3. P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

A. 5511

B. 5611

C. 6511

D. 6611

Answer: Option A

Explanation:

P can complete the work in (12 x 8) hrs. = 96 hrs.

Q can complete the work in (8 x 10) hrs. = 80 hrs.

P's1 hour's work =1

and Q's 1 hour's work =1

.96 80

(P + Q)'s 1 hour's work =1

+1

=11

.96 80 480

So, both P and Q will finish the work in480

hrs.11

Number of days of 8 hours each =480

x1

=60

days = 55

days.11 8 11 11

4. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last? A.6 days B.10 daysC.15 days D.20 days

Answer: Option B

Explanation:

Work done by X in 4 days =1

x 4 =1

.20 5

Remaining work = 1 -1

=4

.5 5

(X + Y)'s 1 day's work =1

+1

=8

=2

.20 12 60 15

Now,2

work is done by X and Y in 1 day.15

So,4

work will be done by X and Y in15

x4

= 6 days.5 2 5

5. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it? A.35 B.40C.45 D.50

Answer: Option B

Explanation:

Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.

Then, 4x + 6y =1

and 3x + 7y =1

.8 10

Solving the two equations, we get: x = 11 , y = 1

400 400

1 woman's 1 day's work =1

.400

10 women's 1 day's work =1

x 10 =1

.400 40

Hence, 10 women will complete the work in 40 days.

6. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C? A.Rs. 375 B.Rs. 400C.Rs. 600 D.Rs. 800

Answer: Option B

Explanation:

C's 1 day's work =1

-1

+1

=1

-7

=1

.3 6 8 3 24 24

A's wages : B's wages : C's wages =1

:1

:1

= 4 : 3 : 1.6 8 24

C's share (for 3 days) = Rs. 3 x1

x 3200 = Rs. 400.24

7. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? A.3 B.5C.7 D.Cannot be determinedE.None of these

Answer: Option C

Explanation:

1 woman's 1 day's work =170

1 child's 1 day's work =1

140

(5 women + 10 children)'s day's work =5

+10

=1

+1

=1

70 140 14 14 7

5 women and 10 children will complete the work in 7 days.

8. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:

A.1

day24

B.7

day24

C.33days

7D.4 days

Answer: Option C

Explanation:

Formula: If A can do a piece of work in n days, then A's 1 day's work =1

.n

(A + B + C)'s 1 day's work =1

+1

+1

=7

.24 6 12 24

Formula: If A's 1 day's work =1

, then A can finish the work in n days.n

So, all the three together will complete the job in 24

days=3

3days.

7 7

9. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone? A.30 days B.40 daysC.60 days D.70 days

Answer: Option C

Explanation:

Let A's 1 day's work = x and B's 1 day's work = y.

Then, x + y =1

and 16x + 44y = 1.30

Solving these two equations, we get: x =1

and y =1

60 60

B's 1 day's work =1

.60

Hence, B alone shall finish the whole work in 60 days.

10. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? A.12 days B.15 daysC.16 days D.18 days

Answer: Option B

Explanation:

A's 2 day's work =1

x 2 =1

.20 10

(A + B + C)'s 1 day's work =1

+1

+1

=6

=1

.20 30 60 60 10

Work done in 3 days =1

+1

=1

.10 10 5

Now,1

work is done in 3 days.5

Whole work will be done in (3 x 5) = 15 days.

11. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in: A.4 days B.6 daysC.8 days D.12 days

Answer: Option B

Explanation:

Suppose A, B and C take x, x

andx

days respectively to finish the work.2 3

Then,1

+2

+3

=1

x x x 2

6=

1

x 2

x = 12.

So, B takes (12/2) = 6 days to finish the work.

12. A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in: A.15 days B.20 daysC.25 days D.30 days

Answer: Option C

Explanation:

(A + B)'s 1 day's work = 110

C's 1 day's work = 1

50

(A + B + C)'s 1 day's work =1

+1

=6

=3

. .... (i)10 50 50 25

A's 1 day's work = (B + C)'s 1 day's work .... (ii)

From (i) and (ii), we get: 2 x (A's 1 day's work) =325

A's 1 day's work =3

.50

B's 1 day's work1

-3

=2

=1

.10 50 50 25

So, B alone could do the work in 25 days.

13. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is: A.15 B.16C.18 D.25

Answer: Option B

Explanation:

Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.

Suppose Tanya takes x days to do the work.

5 : 4 :: 20 : x    x =4 x 20

5

x = 16 days.

Hence, Tanya takes 16 days to complete the work.

14. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:

A.5 days B.6 days

C.10 days D. 101

days2

Answer: Option C

Explanation:

(B + C)'s 1 day's work =1

+1

=7

.9 12 36

Work done by B and C in 3 days =7

x 3 =7

.36 12

Remaining work = 1 -7

=5

.12 12

Now,1

work is done by A in 1 day.24

So,5

work is done by A in 24 x5

= 10 days.12 12

15. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be: A.4 days B.5 daysC.6 days D.7 days

Answer: Option A

Explanation:

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.

Then, 6x + 8y =1

and 26x + 48y =1

.10 2

Solving these two equations, we get : x = 1 and y = 1 .

100 200

(15 men + 20 boy)'s 1 day's work =15

+20

=1

.100 200 4

15 men and 20 boys can do the work in 4 days.

Important Formulas

1. Work from Days:

If A can do a piece of work in n days, then A's 1 day's work =1

.n

2. Days from Work:

If A's 1 day's work =1

, then A can finish the work in n days.n

3. Ratio:

If A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

Simple Interest

1. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is: A.Rs. 650 B.Rs. 690C.Rs. 698 D.Rs. 700

Answer: Option C

Explanation:

S.I. for 1 year = Rs. (854 - 815) = Rs. 39.

S.I. for 3 years = Rs.(39 x 3) = Rs. 117.

Principal = Rs. (815 - 117) = Rs. 698.

2. Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in Scheme B? A.Rs. 6400 B.Rs. 6500C.Rs. 7200 D.Rs. 7500

Answer: Option A

Explanation:

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x).

Then,x x 14 x 2

+(13900 - x) x 11 x 2

= 3508100 100

28x - 22x = 350800 - (13900 x 22)

6x = 45000

x = 7500.

So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400

3. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum? A.Rs. 4462.50 B.Rs. 8032.50C.Rs. 8900 D.Rs. 8925

Answer: Option D

Explanation:

Principal

= Rs. 8925.

4. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

A.3.5 years B.4 years

C.4.5 years D.5 years

Answer: Option B

Explanation:

Time =100 x 81

years = 4 years.

450 x 4.5

5. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

= Rs.100 x 4016.25

9 x 5

= Rs.401625

45

A.3.6 B.6C.18 D.Cannot be determined

Answer: Option B

Explanation:

Let rate = R% and time = R years.

Then,1200 x R x R

= 432100

12R2 = 432

R2 = 36

R = 6.

6. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest? A.3% B.4%C.5% D.6%

Answer: Option D

Explanation:

S.I. = Rs. (15500 - 12500) = Rs. 3000.

Rate =100 x 3000

%= 6%

12500 x 4

7. A person takes a loan of Rs. 200 at 5% simple interest. He returns Rs. 100 at the end of 1 year. In order to clear his dues at the end of 2 years, he would pay: A.Rs. 105 B.Rs. 110

C.Rs. 115 D.Rs. 115.50

Answer: Option C

Explanation:

Amount to be paid

= Rs. 115.

8. An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes: A.10% B.10.25%C.10.5% D.None of these

Answer: Option B

Explanation:

Let the sum be Rs. 100. Then,

S.I. for first 6 months = Rs.100 x 10 x 1

= Rs. 5100 x 2

S.I. for last 6 months = Rs.105 x 10 x 1

= Rs. 5.25100 x 2

So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25

Effective rate = (110.25 - 100) = 10.25%

9. A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is: A.5% B.7%

C. 71

%8

D.10%

Explanation:

Let the rate be R% p.a.

Then, 5000 x R x 2 + 3000 x R x 4 = 2200.

= Rs. 100 +200 x 5 x 1

+100 x 5 x 1

100 100

100 100

100R + 120R = 2200

R =2200

= 10.220

Rate = 10%.

10. A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?A.3.6% B.4.5%C.5% D.6%

Explanation:

Let the original rate be R%. Then, new rate = (2R)%.

Note:

Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. year(s).

725 x R x 1+

362.50 x 2R x 1= 33.50

100 100 x 3

(2175 + 725) R = 33.50 x 100 x 3

(2175 + 725) R = 10050

(2900)R = 10050

R =10050

= 3.462900

Original rate = 3.46%

11. A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:

A.Rs. 2000 B.Rs. 10,000C.Rs. 15,000 D.Rs. 20,000

Answer: Option C

Explanation:

Principal = Rs.100 x 5400

= Rs. 15000.12 x 3

12. A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is: A.5% B.8%C.12% D.15%

Explanation:

S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.

S.I. for 5 years = Rs.2205

x 5 = Rs. 36753

Principal = Rs. (9800 - 3675) = Rs. 6125.

Hence, rate =100 x 3675

%= 12%

6125 x 5

13. What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years? A.1 : 3 B.1 : 4C.2 : 3 D.Data inadequate

Explanation:

Let the principal be P and rate of interest be R%.

Required ratio =

P x R x 6100

=6PR

=6

= 2 : 3.P x R x 9

1009PR 9

14. A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?A.Rs. 35 B.Rs. 245C.Rs. 350 D.Cannot be determined

We need to know the S.I., principal and time to find the rate.

Since the principal is not given, so data is inadequate.

15. A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately

lends it to another person at 6 p.a for 2 years. Find his gain in the transaction per year.

A.Rs. 112.50 B.Rs. 125C.Rs. 150 D.Rs. 167.50

Explanation:

Gain in 2 years = Rs. 5000 x25

x2

-5000 x 4 x 2

4 100 100= Rs. (625 - 400)= Rs. 225.

Gain in 1 year = Rs.225

= Rs. 112.502

Some Important Formulas

1. Principal:

The money borrowed or lent out for a certain period is called the principal or the sum.

2. Interest:

Extra money paid for using other's money is called interest.

3. Simple Interest (S.I.):

If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest.

Let Principal = P, Rate = R% per annum (p.a.) and Time = T years. Then

(i). Simple Intereest =P x R x T

100

(ii). P =100 x S.I.

; R =100 x S.I.

and T =100 x S.I.

.

R x T P x T P x R

Some Important Formulas

Time and Distance

1. Speed, Time and Distance:

Speed =Distance

, Time =Distance

, Distance = (Speed x Time).Time Speed

2. km/hr to m/sec conversion:

x km/hr = x x5

m/sec.18

3. m/sec to km/hr conversion:

x m/sec = x x18

km/hr.5

4. If the ratio of the speeds of A and B is a : b, then the ratio of the

the times taken by then to cover the same distance is1

:1

or b : a.a b

5. Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. Then,

the average speed during the whole journey is2xy

km/hr.x + y

Some Important FormulasCLOCK

1. Minute Spaces:

The face or dial of watch is a circle whose circumference is divided into 60 equal parts, called minute spaces.

Hour Hand and Minute Hand:

A clock has two hands; the smaller one is called the hour hand or short hand while the larger one is called minute hand or long hand.

2.i. In 60 minutes, the minute hand gains 55 minutes on the hour on the hour

hand.

ii. In every hour, both the hands coincide once.

iii. The hands are in the same straight line when they are coincident or opposite to each other.

iv. When the two hands are at right angles, they are 15 minute spaces apart.

v. When the hands are in opposite directions, they are 30 minute spaces apart.

vi. Angle traced by hour hand in 12 hrs = 360°

vii. Angle traced by minute hand in 60 min. = 360°.

viii. If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast.

On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.

Some Important FormulasCalendar

1. Odd Days:

We are supposed to find the day of the week on a given date.

For this, we use the concept of 'odd days'.

In a given period, the number of days more than the complete weeks are called odd days.

2. Leap Year:

(i). Every year divisible by 4 is a leap year, if it is not a century.

(ii). Every 4th century is a leap year and no other century is a leap year.

Note: A leap year has 366 days.

Examples:

i. Each of the years 1948, 2004, 1676 etc. is a leap year.ii. Each of the years 400, 800, 1200, 1600, 2000 etc. is a leap year.

iii. None of the years 2001, 2002, 2003, 2005, 1800, 2100 is a leap year.

3. Ordinary Year:

The year which is not a leap year is called an ordinary years. An ordinary year has 365 days.

4. Counting of Odd Days:

1. 1 ordinary year = 365 days = (52 weeks + 1 day.)

1 ordinary year has 1 odd day.

2. 1 leap year = 366 days = (52 weeks + 2 days)

1 leap year has 2 odd days.

3. 100 years = 76 ordinary years + 24 leap years

  = (76 x 1 + 24 x 2) odd days = 124 odd days.

  = (17 weeks + days) 5 odd days.

Number of odd days in 100 years = 5.

Number of odd days in 200 years = (5 x 2) 3 odd days.

Number of odd days in 300 years = (5 x 3) 1 odd day.

Number of odd days in 400 years = (5 x 4 + 1) 0 odd day.

Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years etc. has 0 odd days.

2. Day of the Week Related to Odd Days:

No. of days:

0 1 2 3 4 5 6

Day:Sun.

Mon.

Tues.

Wed.

Thurs.

Fri.

Sat