Let third side of an isosceles triangle be x.
Then two other equal sides are twice.
So, the both equal sides are 2x and 2x.
Here, perimeter = 30 cm as perimeter is addition of lengths of all sides.
So, x + 2x + 2x = 30  \(\Rightarrow\) 5x = 30
On dividing both sides by 5, we get
          \(\frac{5x}{5}=\frac{30}{5}\Rightarrow\) x = 6cm
\(\therefore\)  Third side = x = 6 cm
So, the other equal sides are 2x and 2x = 2 x 6 and 2 x 6 = 12 cm and 12 cm.

Let his total journey length be x km.
\(\therefore\) Travelled by train = \(\frac{2}{5}x,\) travelled by bus = \(\frac{1}{3}x\) and travelled by car = \(\frac{1}{4}x\)
\(\therefore\) Total journey travelled by train, bus and car
               = \(\frac{2}{5}x+\frac{1}{3}x+\frac{1}{4}x\)
               = \(\frac{12\times 2x+20\times x+15\times x }{60}\)
               = \(\frac{24x+20x+15x}{60}=\frac{59x}{60}\)
\(\therefore\) Remaining = \(\frac{x}{1}-\frac{59x}{60}=\frac{60x-59x}{60}=\frac{x}{60}\)
According to the question, remaining journey is 3 km.
\(\therefore \quad \frac{x}{60}=3\Rightarrow x=3\times60=180\)
Hence, the length of his total journey is 180 km.

(i) Let the number be x.
Now, 1 is subtracted from a number, then
(x -1), the difference is multiplied by \(\frac{1}{2}\)
Here, \(\frac{1}{2}\) (x - 1) gives result 7
\(\therefore \frac{1}{2}(x-1)=7\)
(ii) Let age of Soh an be x yr. Then, the age of
Mohan is (x + 3) yr.
\(\therefore\) Sum of their ages = 43
\(\Rightarrow\)   x+(x+ 3)=43
(iii) Let the number be x. Then, five times of number be 5x.
Since it is increased by 7.
So, 5x + 7 gives result 27.
Hence, the equation is 5x + 7 = 27.

Let x be the interest received by Ramesh.
So, interest received by Karim = Rs (x + 13000)
The total interest received by both of them = Rs 17000
\(\therefore\) x + x + 13000 = 17000  \(\Rightarrow\) 2x = 17000 - 13000
            2x = 4000 \(\Rightarrow x=\frac{4000}{2}=\) Rs 2000
Karim received interest = 2000 + 13000 =  Rs 15000
\(\therefore\) karim gives \(\frac{1}{2}\)th of his interest to Ramesh
                 = \(\frac{15000}{2}=\) Rs 7500
Karim is very helping to his friend.

As per the given information in the question, the total number of students in the class = 60
Let x be the number of boys in the class.
So, the number of girls in the class = \(\frac{x}{3}\)
\(\therefore x+\frac{x}{3}=60\Rightarrow \frac{3x+x}{3}=60\Rightarrow \frac{4x}{3}=60\)
4x = 60 x 3  \(\Rightarrow\) 4x = 180 \(\Rightarrow x=\frac{180}{4}=45\)
Hence, the number of boys in the class is 45 and number of girls in the class is \(\frac{45}{3}=15\)

Let x be the number. So, half of x is \(\frac{x}{2}\)
Then, \(\frac{x}{2}+45=3x\Rightarrow \frac{x+90}{2}=3x\)
     x + 90 = 6x  \(\Rightarrow\) 90 = 5x  \(\Rightarrow \quad x=\frac{90}{5}=18\)
Hence, the number is 18.

As per the given information in the question, the perimeter of a rectangle is 40 m.
        [ \(\therefore\) Perimeter of rectangle = 2 length + 2 breadth]
Let x be the breadth of the rectangle.
Then, length of the rectangle = 5x - 4
\(\therefore\)     2x + 2(5x - 4) = 40
\(\Rightarrow\)       2x + 1Ox - 8 = 40
\(\Rightarrow\)       12x = 48 \(\Rightarrow\) x = 4
Hence, length of the rectangle
= 5x - 4 = (5 x 4) - 4 = 20 - 4 = 16 m.

Let x be the age of Amit.
So, age of Sohan Lal, the father of Amit = 4x yr
If the difference of their ages is 27 yr.
Then, 4x- x = 27 \(\Rightarrow\) 3x = 27 \(\Rightarrow x=\frac{27}{3}=9\)
Hence, age of Amit is 9 yr.

-16

X - V = V.