Question : If 80% of A is 13 more than 90% of B, and the ratio of 40% of A to 60% of B is 10 : 9, then what is the value of A – B?
Option 1: 50
Option 2: 80
Option 3: 20
Option 4: 60
Correct Answer: 20
Solution :
From the first condition,
$0.8A = 0.9B + 13$ ___(1)
From the second condition,
$\frac{0.4A}{0.6B} = \frac{10}{9} \Rightarrow 0.4A = \frac{10}{9} \times 0.6B$ ___(2)
From equation (2), we can express A in terms of B:
$A = \frac{10}{9} \times \frac{0.6B}{0.4} = \frac{5}{3}B$ ___(3)
Substitute equation (3) into equation (1):
$0.8 \times \frac{5}{3}B = 0.9B + 13 $
$\Rightarrow 13B = 390$
$\Rightarrow B =30$
Substitute B into equation (3) to find A,
$A = \frac{5}{3} \times 30= 50$
Therefore, the value of A - B is:
$A - B = 50 - 30 = 20$
Hence, the correct answer is 20.
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