In a cricket team of eleven players, one player weighing 42 kg is injured and his place is taken by another player. If the average by another player. If the average by 100 grams as a result of this,then the weight of the new player is:

Solution
Weight of the new player
\(=\left ( 42+\frac{11\times 100}{1000} \right )kg\)
= 43.1 kg
9 men went to a hotel. 8 of them spent Rs. 30 each over their meals and the 9th spent Rs. 20 more than the average expenditure of all the nine. The total money spent by them is :

Solution
Let the total money spent be Rs. x.
According to the question,
^{x}⁄_{y} + 20 +30 × 8 = x
⇒x^{x}⁄_{9}=260
\(∴x=\frac{260\times 9}{8}\)
= Rs. 292.50
The average age of a family of 5 members is 24 years. If the age of youngest member be 6 years,find the average age of the family at the birth of the youngest member.

Solution
Sum of the ages of 4 members 6 years ago
=24×56×5=90 years
∴ Required average = ^{90}⁄_{5}
= 18 years
Of the three numbers whose average is 60, the first is one fourth of the sum of the others. The first number is :

Solution
x+ y + z = 180 (1)
According to the question,
x=\(\frac{180x}{4}\)
⇒ 4x+ x= 180 ⇒ 5x= 180
\(\Rightarrow x=\frac{180}{5}=36\)
Of the three numbers, second is twice the first and is also thrice the third. If the average of the three numbers is 44, the largest number is :

Solution
Let the largest number i.e, second number is x then first
number =^{x}⁄_{2} and third =^{x}⁄_{3}
⇒ From question ^{x}⁄_{2} + x +^{x}⁄_{3} = 44
⇒\(\frac{11x}{6}=44\)
⇒\(x=\frac{44}{11}\times 6=24\)
The average temperature for Monday, Tuesday and Wednesday was 40°C. The average for Tuesday, Wednesdayand Thursday
was 41°C. If on Thursday temperature is 45°C, what was it on Monday?

Solution
M + T + W = 120......(i)
T + W + Th = 41 × 3
⇒ T + W = 123  45 = 78 ...(ii)
From equation (i) (ii).
M = 120 78 = 42°C
The average expenditure of a man for the first five months is Rs. 1200 and for the next seven months is Rs. 1300. Find his monthly average income if he saves Rs. 2900 during the year ?

Solution
Man's annual income
= Rs. [(1200 × 5 + 1300 × 7) + 2900]
= Rs. (6000 + 9100 + 2900)
= Rs. 18000
∴ Man's monthly average income
= Rs.\(\left ( \frac{18000}{12} \right )\)
= Rs. 1500
12 men and 18 boys working 7^{1}⁄_{2} hours a day can do a certain work in 60 days. If one man
works equal to 2 boys, then the number of bOYS required to help 21 men to do twice the work in 50 days, working 9 hours a day, will be

Solution
Let x boys be required.
12m + 18b = 42b
21m + xb = (42 + x)b
Working Days Work Boys hours/day
\(\Rightarrow \frac{42+x}{42}=\frac{2}{1}\times \frac{60}{50}\times \frac{15/2}{9}\)
∴42 + x
\(=\frac{15 \times 42 \times 60}{9\times 50}= 84\)
∴ x = 84  42 = 42
A certain number of men can do a work in 60 days. If there were 8 men more it could be finished in 10 days less. How many men were there in the beginning?

Solution
∴ 50 : 60 = x : x + 8
⇒ 6x= 5 (x « 8)
⇒ 6x5x= 40
⇒x=40
A certain job was assigned to a group of men to do in 20 days. But 12 men did not turn up for the job and the remaining men did the job in 32 days. The original number of men in the group was

Solution
Let the original number of men be X.
Now,
∴ 32: 20 = x : x  12
⇒ 20x = 32 (x 12)
⇒ 5x = 8 (x 12)
⇒ 8x 5x= 96
⇒ 3x= 96
⇒ X=^{96}⁄_{3}=32