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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