SSC MTS 2022 Question Paper Shift 3 (July 20th)

Question 56

If 3a: 2b = (6a - 3) : (3b - 2) and a = b - 1, then what will be the value of 12ab?

Solution

If 3a: 2b = (6a - 3) : (3b - 2)

$$\frac{3a}{2b}=\ \frac{(6a-3)}{(3b-2)}$$

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

a(3b-2) = 2b(2a-1)
3ab-2a = 4ab-2b
2b-2a = 4ab-3ab
2b-2a = ab
2(b-a) = ab   Eq.(i)
a = b - 1
b - a = 1    Eq.(ii)
Put Eq.(ii) in Eq.(i).
2 = ab
Value of 12ab = $$12\times2$$
= 24

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