National Jobs Preparation: Word Problems Mathematics for the post of (LDC UDC ASSISTANT STENO SUB ENGINEER)

Word problems

The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?

31 29

28 30

Correct Answer: A. 31

Total score of the batsman in 20 matches = 800.

The total score of the batsman in the next 10 matches = 130.

The total score of the batsman in the 30 matches = 930.

Average score of the batsman = 930/30 = 31

The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?

A. Rs. 25

B. Rs. 18

C. Rs. 15

D. Rs. 22

Correct Answer: C. Rs. 15

Total members in the group = 7

Average amount = Rs. 20

Total amount with them = 7 * 20 = Rs. 140

One number has Rs. 50. So, the amount with remaining 6 people = 140 – 50 = Rs. 90

The average amount with them = 90/6 = Rs. 15

The sum of five numbers is 655.

The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?

180

170

190

175

Correct Answer: A. 180

Let the five numbers be P, Q, R, S and T.

=>P+Q+R+S+T=655.

(P + Q)/2 = 85 and R = 125

P + Q = 170 and R = 125

P+Q+R=295

S+T=655–(P+Q+R)=360

Average of the last two numbers = (S + T)/2 = 180

Find the average of the series : 312, 162, 132, 142 and

122? A. 194

B. 174

C. 162

D. 186

Correct Answer: B. 174

Average = (312 + 162 + 132 + 142 + 122)/5 = 870/5 = 174

The average age of a group of 10 persons was decreased by 3 years when one person, whose

age was 42 years, was replaced by a new person. Find the age of the new person?

Correct Answer: C. 12

The initial average age of the 10 persons is P.

Age of the new person Q. Sum of the ages of the initial 10 persons = 10P

New average = (P-3) 10(P-3) = 10P – 42 + Q => Q = 12

The average of the marks of 12 students in a class is 36. If the marks of each student are doubled,

find the new average?

Correct Answer: A. 72

Sum of the marks for the 12 students = 12 * 36 = 432. The marks of each student are doubled,

the sum also will be doubled.

The new sum = 432 * 2 = 864. So, the new average = 864/12 = 72

The average of 10 numbers is 23. If each number is increased by 4, what will the new average

be? A. 22

B. 27

C. 25

D. 29

Correct Answer: B. 27

Sum of the 10 numbers = 230

If each number is increased by 4, the total increase =

4*10=40

The new sum = 230 + 40 = 270 The new average = 270/10 = 27

The average of 35 numbers is 25. If each number is multiplied by 5, find the new

average? A. 96

B. 125

C. 140

D. 168

Correct Answer: B. 125

Sum of the 35 numbers = 35 * 25 = 875

If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets

multiplied by 5.

Thus, the new average = 25 * 5 = 125

The average marks of a class of 30 students is 40 and that of another class of 50 students is

60. Find the average marks of all the students?

47.5

52.5

Correct Answer: D. 52.5

Sum of the marks for the class of 30 students = 30 * 40 = 1200

Sum of the marks for the class of 50 students = 50 * 60 = 3000

Sum of the marks for the class of 80 students =

1200 + 3000 = 4200

Average marks of all the students = 4200/80 = 52.5

A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3.

Find his average after the 16th inning?

Correct Answer: C. 19

Let the average after the 16th inning be P.

So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64 = 16P => P = 19

The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is

61. Find the 8th number?

Correct Answer: A. 46

Sum of all the 13 numbers = 13 * 60 = 780

Sum of the first 7 of them = 7 * 57 = 399

Sum of the last 7 of them = 7 * 61 = 427

So, the 8th number = 427 + 399 – 780 = 46

Find the average of the first 20 natural

numbers? A. 10

B. 11.5

C. 12

D. 10.5

Correct Answer: D. 10.5

Average of the first ‘n’ natural numbers = (n + 1)/2

We get (20 + 1)/2 = 10.5

The average of 11 results is 50, if the average of first six results is 49 and that of the last six is

52. Find the sixth result?

Correct Answer: B. 56

1 to 11 = 11 * 50 = 550

1 to 6 = 6 * 49 = 294

6 to 11 = 6 * 52 = 312

6th = 294 + 312 – 550 = 56

The average of five results is 46 and that of the first four is 45. The fifth result

is: A. 1

B. 10

C. 12.5

D. 50

Correct Answer: D. 50

5*46–4*45=50

Three years ago the average age of a family of six members was 19 years. A boy have been

born, the average age of the family is the same today. What is the age of the boy?

A. 1 year

B. 1.5 years

C. 2 years

D. 2.5 year

Correct Answer: A. 1 year

6*22=132

7*19=133

—————–

133 -132 = 1 Year

Nine men went to a hotel. Eight of them spent Rs.3 each over their meals and the ninth spent Rs.2 more than the average expenditure of all the nine. Determine the total money spent by them?

Rs.29.25

Rs.30.25

Rs.32

Rs.35

Correct Answer: A. Rs.29.25

Average of 9 = x

9x = 8 * 3 + x * 2 x = 3.25

Total = 9 * 3.25 = 29.25

The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?

A. 7 years

B. 11 years

C. 18 years

D. 27 years

Correct Answer: C. 18 years

9 * 2 = 18 years

A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3.

What is his average after the 17th innings?

Correct Answer: D. 37

16x + 85 = 17 (x + 3)

x = 34 + 3 = 37

The average age of M boys is ‘b’ years and of ‘n’ girls ‘c’ years. The average age of all together

is:

A. (mb – nc)/ (m + n) years

B. (mb + nc)/ (m – n) years

C. (mb + nc)/ (m + n) years

D. (mb – nc)/ (m – n) years

Correct Answer: C. (mb + nc)/ (m + n) years

A team of eight entered for a shooting competition. The best marks man scored 85 points. If

he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?

625

665

632

656

Correct Answer: B. 665

8*84=672–7=665

The average salary of workers in an industry is Rs.200 the average salary of technicians

being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers?

250

275

550

400

Correct Answer: C. 550

The average age of 8 men increases by 2 years when two women are included in place of two

men of ages 20 and 24 years. Find the average age of the women?

A. 36 years

B. 24 years

C. 30 years

D. 18 years

Correct Answer: C. 30 years

20+24+8*2=60/2=30

The average of first five prime numbers greater than 20

is: A. 31.00

B. 31.01

C. 32.00

D. 32.2

Correct Answer: D. 32.2

Detail About MCQs+

23+29+31+37+41=161/5=32.2

The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being

8. What was the 5th observation?

Correct Answer: D. 9

1 to 9 = 9 * 9 = 81

1 to 5 = 5 * 10 = 50

5 to 9 = 5 * 8 = 40

5th = 50 + 40 = 90 – 81 = 9

The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the

last number is 13. What is the last numbers?

Correct Answer: C. 5

A+B+C=48

B+C+D=45

A+D=13

A–D=3

A+D=13

2D=10

D = 5

The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age

in years of the youngest boy?

Correct Answer: A. 9

3x + 5x + 7x = 45

3x = 9

The average of first 10 odd numbers

is: A. 11

B. 10

C. 12

D. 17

Correct Answer: B. 10

Sum of 10 odd no. = 100

Average = 100/10 = 10

The average of first 10 natural numbers

is: A. 5

B. 5.5

C. 6.5

D. 6

Correct Answer: B. 5.5

Sum of 10 natural no. = 110/2 = 55

Average = 55/10 = 5.5

The average of first ten prime numbers which are odd

is: A. 12.9

B. 13.8

C. 15.8

D. 17

Correct Answer: C. 15.8

3,5,7,11,13,17,19,23,29,31

Average = 3+5+7+11+13+17+19+23+29+31/10

158/10

15.8

The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is

11.4 the sixth number is:

11.0

11.3

11.4

11.5

Correct Answer: D. 11.5

Sum of 11 numbers = 11×10.9 = 119.9

Sum of 1st 6 numbers = 6×10.5 = 63

So, sum of last 5 numbers = 119.9-63 = 56.9

And sum of last 6 numbers = 6×11.4 = 68.4

Hence sixth number will be = 68.4-56.9= 11.5

The average of first 10 even numbers

is: A. 18

B. 22

C. 9

D. 11

Correct Answer: D. 11

Two automobiles are 150 kilometers apart and traveling toward each other. One automobile

is moving at 60km/h and the other is moving at 40km/h mph. In how many hours will they meet?

2.5

2.0

1.75

1.5

Correct Answer: D. 1.5

One moves at 60km/h, so in an hour, he’ll travel 60km

The other moves at 40km/h, so in an hour, he’ll travel 40km

This is towards each other, so, in an hour, we can say that they’ll get 60+40=100km closer.

This means that they get closer at 100km/h

Given that we have a distance of 150km, and the speed of closure at 100kmh, we can now use

the equation

S=D/T

Rearrange to find T (times both sides by T)

S x T = D (now divide both sides by S)

T=D/S

Time = 150km divided by 100km/h

Time = 1.5 hours

Or one hour and 30 minutes

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then

the average marks of all the students is:

53.33

54.68

Correct Answer: B. 54.68

55 students get average marks of 55%.

so 55*50=2750

Similarly 60*55=3300

& 60*45=2700 now total no of marks obtain by all students of three batches= 2750+3300+2700=8750/= Total no of students= 55+60+45=160. By dividing total marks on each student, we get average marks obtain by each student so 8750/160 = 54.68