Question : Directions: Two persons A and B get the same salary. Their basic pay is different. The allowances are 65% and 80% of the basic pay respectively. What is the ratio of the basic pay?
Option 1: 17 : 15
Option 2: 7 : 5
Option 3: 11 : 10
Option 4: 12 : 11
Correct Answer: 12 : 11
Solution :
Given:
Two persons A and B get the same salary.
Their basic pay is different.
The allowances are 65% and 80% of the basic pay respectively.
Let's consider that A's basic pay is X and B's is Y.
As per the given details,
Allowances of A = 65% of basic pay
Salary of A = X + 65% of X
⇒ X + (65 ÷ 100) × X
⇒ X + (65X) ÷ 100
⇒ (100X + 65X) ÷ 100
⇒ 165X ÷ 100
Allowances of B = 80% of basic pay
Salary of B = Y + 80% of Y
⇒ Y + (80 ÷ 100) × Y
⇒ Y + (80Y) ÷ 100
⇒ (100 + 80Y) ÷ 100
⇒ 180Y ÷ 100
Again, it is given that both salaries are equal.
Therefore,
165X ÷ 100 = 180Y ÷ 100
⇒ 165X = 180Y (cancelling 100 on both sides denominators)
⇒ X ÷ Y = 180 ÷ 165
⇒ X : Y = 180 : 165
⇒ X : Y = 12 : 11
So, the ratio of the basic pay is 12 : 11. Hence, the fourth option is correct.
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