ans: Average mark of the 10% of students excluded from the group is 35 marks.
Average mark obtained by 300 students in a class = 80
Total marks of 300 students = 300 x 80 = 24000
Given that when 10% of the students are excluded from the group,
the average mark of remaining students is 85
Total 10% of the excluded students = 300 x 10% = 30
remaining students = 300 – 30 = 270
So, the total marks of remaining 270 students = 270 x 85 = 22950
The total marks of excluded 10% students = 24000 – 22950 = 1050
So, the average mark of 10% excluded students = 1050 + 30 = 35 marks.
ans: 6 grams gold will need to be added to make the ratio of gold and silver 5 : 3.
The amount of gold in the ornament is = (42 x$\frac{4}{7}$) = 24 grams
The amount of silver in the ornament is = 42 – 24 = 18 grams
Let, x grams of gold to be added to make the ratio 5 : 3
According to question, $\frac{24+x}{18}$ = $\frac{5}{3}$
=> 72 + 3x = 90
=> 3x = 90 – 72
=> 3x = 18
x = 6
ans: 60 hours time is needed for the leak to empty the cistern.
As the cistern can be filld in 10 hours but it takes 12 hours due to a leak in its bottom
Work done by the cistern in 1 hour = ($\frac{1}{10} -\frac{1}{12}$)
= $\frac{6-5}{60}$
= $\frac{1}{60}$
$\frac{1}{60}$ Part of the cistern is emptied in 1 hour
1 or Full part of the cisterm is emptied in =$\frac{1×60}{1}$ = 60 hours
ans : $\frac{2}{5}$
$\frac{8}{2x-1}+\frac{9}{3x-1}$ = $\frac{7}{x+1}$
=>$\frac{8}{2x-1}+\frac{9}{3x-1}$ = $\frac{4+3}{x+1}$
=>$\frac{8}{2x-1}+\frac{9}{3x-1}$ = $\frac{4}{x+1}+\frac{3}{x+1}$
=>$\frac{8}{2x-1}-\frac{4}{x+1}=\frac{3}{x+1}\frac{9}{3x-1}$
=>$\frac{8x+8-8x+4}{(2x-1)(x+1)}=\frac{9x-3-9x-9}{(x+1)(3x-1)}$
=>$\frac{1}{(2x-1)(x+1)}=\frac{-1}{(x+1)(3x-1)}$
=>-(2x-1)=(3x-1)
=> 3x+2x = 1+1
=> 5x=2
x = $\frac{2}{5}$
