Question 65
If (x + 10)% of 200 is $$33\frac{1}{3}\%$$ more than x% of 180, then 10% of (x + 20) is what percent less than 40% of x?
Solution
If (x + 10)% of 200 is $$33\frac{1}{3}\%$$ more than x% of 180.
$$(x+10)\ \%\ of\ 200=\frac{4}{3}\ of\ x\%\ of\ 180$$
2(x+10) = 2.4x
(x+10) = 1.2x
0.2x = 10
x = 50
10% of (x + 20) = 10% of (50+ 20) = 7 Eq.(i)
40% of x = 40% of 50 = 20 Eq.(ii)
So Eq.(i) is 13 less than Eq.(ii)
Percent less = $$\frac{13\ \times\ 100}{20}$$
= 65%
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