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The following question based on average topic of quantitative aptitude

Questions : The average weight of 15 oarsmen in a boat is increased by 1.6 kg when one of the crew, who weighs 42 kg is replaced by a new man. Find the weight of the new man (in kg).

(a) 66

(b) 43

(c) 65

(d) 67

The correct answers to the above question in:

Answer: (a)

Using Rule 18,

If in the group of N persons, a new person comes at the place of a person of ‘T’ years, so that average age, increases by ‘t’ years

Then, the age of the new person = T + N.t

If the average age decreases by ‘t’ years after entry of new person, then the age of the new person = T – N.t

Here, N = 15, T = 42, t = 1.6

Weight of new oarsman

= (42 + 15 × 1.6) kg.

= (42 + 24) kg. = 66 kg.

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Read more simple average Based Quantitative Aptitude Questions and Answers

Question : 1

Six tables and twelve chairs were bought for Rs.7,800. If the average price of a table is Rs.750, then the average price of a chair would be

a) Rs.150

b) Rs.175

c) Rs.275

d) Rs.250

Answer: (c)

Average cost of a chair

=Rs. x, then

x × 12 + 6 × 750 = 7800

⇒ 12x = 7800 – 4500 = 3300

⇒ x = $3300/12$ = Rs. 275

Question : 2

The average monthly expenditure of a family is Rs.2,200 during first three months,Rs.2,550 during next four months and Rs.3,120 during last five months of the year. If the total savings during the year was Rs.1,260, what is the average monthly income ?

a) Rs.2,805

b) Rs.2,850

c) Rs.1,280

d) Rs.1,260

Answer: (a)

Using Rule 1,

Average of two or more numbers/quantities is called the mean of these numbers, which is given by

$\text"Average(A)" = \text"Sumof observation / quantities"/\text"No of observation / quantities"$

∴ S = A × n

Total expenditure of the year

= Rs.(3 × 2200 + 4 × 2550 + 5 × 3120)

= Rs. (6600 + 10200 + 15600)

= Rs.32400

∴ Total income of the year

= Rs. (32400 + 1260)

= Rs.33660

∴ Average monthly income

= Rs.$33660/12$ = Rs. 2805

Question : 3

There are two groups A and B of a class, consisting of 42 and 28 students respectively. If the average weight of group A is 25 kg and that of group B is 40 kg, find the average weight of the whole class.

a) 70 kg

b) 30 kg

c) 31 kg

d) 69 kg

Answer: (c)

Required average weight

= ${42×25+28×40}/{42+28}$

= ${1050+1120}/70$ = $2170/70$ = 31kg

Aliter : Using Rule 10,

Here, $n_1$ = 42, $a_1$ = 25

$n_2$ = 28, $a_2$ = 40

∴ Average = ${n_1a_1+ n_2a_2}/{n_1+ n_2}$

Question : 4

Six friends have an average height of 167 cms. A boy with height 162 cm leaves the group. Find the new average height.

a) 169 cm

b) 167 cm

c) 166 cm

d) 168 cm

Answer: (d)

Total height of 5 friends

= (6 × 167 – 162) cm.

= (1002 – 162) cm.

= 840 cm.

∴ Required average = $840/ 5$

= 168 cm.

Question : 5

Numbers of boys and girls are ‘x’ and ‘y’ respectively. Ages of a girl and a boy are ‘a’ years and ‘b’ years respectively. The average age (in years) of all boys and girls is

a) $\text"x+y"/\text"bx+ay"$

b) $\text"x+y"/\text"bx+ay"$

c) $\text"bx+ay"/\text"x+y"$

d) $\text"x+y"/\text"ax+by"$

Answer: (c)

According to question,

Total age of boys = ap years

Total age of girls = bq years

∴ Required average =${ap + bq}/{p +q}$

Question : 6

If the average of m numbers is $n^2$ and that of n numbers is $m^2$, then average of (m + n) numbers is

a) $m/n$

b) m+n

c) mn

d) m-n

Answer: (c)

The average of m numbers = n2

Total number of ‘m’ numbers = m × n²

And the average of n numbers = m2

Total number of ‘n’ numbers = n × m²

∴ Average of (m + n) numbers

= ${mn² + m²n}/{m + n} = {mn(n + m)}/{m + n} = mn$

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