Madhya Pradesh Police Exam Model Paper 7

Given:
First : second = 2 : 3
Second : third = 6 : 5
First × third = 1620
Calculation:
Let third is = 5m
Second = 6m
First = 6m/3 × 2 ⇒ 4m
First × third = 1620
$\Rightarrow 4\mathit{m}\times 5\mathit{m}=1620$
$\Rightarrow 20{\mathit{m}}^2=1620$
$\Rightarrow {\mathit{m}}^2=81$
⇒ m = 9
First = 4m ⇒ 4 × 9 ⇒ 36
Second = 6m ⇒ 6 × 9 ⇒ 54
Third = 5m ⇒ 5 × 9 ⇒ 45
Difference between second and third = 54 — 45 ⇒ 9
Let us combine the two ratios to get one single ratio between first, second, and third numbers.
Ratio between first and second number × 2 = 4 ∶ 6
Now combining the two ratios we get, first ∶ second ∶ third = 4 ∶ 6 ∶ 5
Product of first and third = 4 unit × 5 unit = 1620
1 unit = √(1620/20) = 9
Difference between second and third number = 6 unit - 5 unit = 1 unit = 9
∴ The required difference is 9.