Question

If (a + b) : (a - b) is equal to the duplicate ratio of 3 : 1 then a : b is?

Answer 1

componendo dividendo rule for

a/b = x/y is a+b/a-b = x+y/x-y

duplicate ratio of 3:1 =3²:1² = 9:1

a + b / a-b = 9/1

applying componendo dividendo rule

a/b = 9+1/9-1

=10/8=5/4 = 5:4

answer is c

Answer 2

Answer:

value of $a : b$ is $2: 1$ .

Step-by-step explanation:

To find : value of $a : b$

Given  : (a + b) : (a - b) is equal to the duplicate ratio of $3 : 1$ .

Solution  :

• As per given data we know that  (a + b) : (a - b) is equal to the duplicate ratio of $3 : 1$ .
• According to given condition we can write as , $(a + b) : (a - b) = 3 : 1$ .
• We know that ratios can be written in form fractions . Hence we get ,   $\frac{a + b}{a -b} = \frac{3}{1}$
• By cross multiplying denominators of LHS and RHS , and performing arithmetic operations we find the value of $a$ and $b$ .

        $\frac{a + b}{a -b} = \frac{3}{1} \\\\1 (a +b )= 3 ( a -b )\\\\a + b = 3a -3b \\\\3b + b =3a -a \\\\4b = 2a \\\\\frac{4}{2} = \frac{a}{b}\\\\\frac{a}{b}= \frac{2}{1}$