Exercise: 9.2
Question 1
Let the required number = x
5 times the number = 5x
7 added to 5 times the number = 5x + 7
According to the problem
$5 x+7=57$
$5 x=50$
$x=50 / 5$
$x=10$
Question 2
Let the required number = x
$\frac{1}{4}^{\text {th }}$ of the number is 3 more than 7
$\frac{1}{4} x=7+3$
$\frac{1}{4} x=10$
$\quad x=40$
Question 3
Let required number = x
A number is greater than 15 and it is Less than 51 then
x - 15 = 51 -x
2x = 66
x = 33
Question 4
Let required number = x
$\frac{1}{2}$ is subtracted from a number = $x-1 / 2$
Multiplied by 4 = $4(x-1 / 2)$
Given result = 5
$4(x-1 / 2)=5$
$24\times\left(\frac{2 x-1}{y}\right)=5$
$4 x-2=5$
$4 x=5+2$
$4 x=7$
$x=7 / 4$
Question 5
Let the required number = x , 80- x
The greater number exceeds twice the smaller by 11 is
$x=2(80-x)+11$
$x=160-2 x+11$
$3 x=171$
$x=171 / 3$
x=57 And other number is 80 - 57 = 23
Question 6
Three consecutire odd natureal number are
$2 x+1, \quad 2 x+3, \quad 2 x+5$
Given sum is = 87
$2 x+2 x+3+2 x+5=87$
$6 x=87-9$
$6 x=78$
$x=78 / 6$
x = 13
Required number are 27, 29 , 31
Question 7
Let number of boys = x
Number of girls = $\frac{2}{5} x$.
Total no. of students = 35
$x+\frac{2}{5} x=35$'
$5 x+2 x=35 \times 5$
$7 x=35 \times 5$''
$x=\frac{35 \times 5}{7}$
$x=25$
Number of girls in the class is = $\frac{2}{5} \times 25$ = 10
Question 8
Let number of chairs = x
A house wife purchased certain number of chairs and two tables = 2800
$(250 \times x)+(2 \times 400)=2800$
$(250 \times x)+(800)=2800$
$250 \times x=2800-800$
$x=\frac{2000}{250}$
$x=8$
Number of chairs purchased = 8
Question 9
Let Aparna's monthly salary= x
Then over time payment = x - 16560
According to the problem
$\begin{aligned} x+x-16560 &=27840 \\ & 2 x=44,400 \\ &=\frac{44,400}{2} . \\ x=& 22,200 \end{aligned}$
Aparna monthly salary= 22,200
Question 10
Let 5 rupee coins = x
2 rupees coins = 80 -x
According to the problem total amount is 232 rupees
$\begin{aligned} 5 x+2(80-x) &=232 \\ 5 x+160-2 x &=232 \\ 3 x &=232-160 \\ 3 x &=72 \\ x=& 72 / 3 \\ x &=24 \end{aligned}$
Number of 5 rupees coins = 24
Question 11
Let purse contains 10 rupees notes = x
50 rupees notes is one less = x - 1
According to the problem total amount in purse is = 550
$10 x+50(x-1)=550$
$10 x+50 x-50=550$
$60 x=600$
$x=600 / 60$
$x=10$
Number of 50 rupees note = 10-1 = 9
Question 12
Let present age = x
After 12 years = x + 12
3 Times as old was 4 years ago
$x+12=3(x-4)$
$x+12=3 x-12$
$2 x=24$
$x=24 / 2$
$x=12$
Present age is 12
Question 13
Given sides of isosceles triangle are
$3 x-1, \quad 2 x+2,2 x$
Two equal sides are
$3 x-1=2 x+2$
$3 x-2 x=2+1$
$x=3$
perimeter of triangle $=3 x-1+2 x+2+2 x$
$=7 x+1$
$=7(3)+1$
$=22$
Question 14
Let breadth = x
Length of the rectanangular = 3x - 6
According to the problem perimeter is = 148
$\begin{aligned} 2(x+3 x-6) &=148 \\ 2(4 x-6) &=148 \\ 8 x-12 &=148 \\ 8 x &=160 \\ x &=80 \end{aligned}$
Length 54 , breadth = 20
Question 15
Difference of each angle = 20 '
Let the angles be = x and x + 20
Sum of the complementary angle is 90'
$x+x+20=90$
$2 x=90-20$
$2 x=70$
$x=35$
One angles , 35' other angle is (35+ 20) = 5
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