Question : If decreasing 110 by $x$% gives the same result as increasing 50 by $x$%, then $x$% of 650 is what percentage more than ($x$ + 20)% of 180? (correct to the nearest integer)
Option 1: 136%
Option 2: 90%
Option 3: 154%
Option 4: 80%
Correct Answer: 136%
Solution : According to the question, $110 \times \frac{100 - x}{100} = 50 \times \frac{100 + x}{100}$ ⇒ $11 \times (100 - x) = 5 \times (100 + x)$ ⇒ $1100 - 11x = 500 + 5x$ ⇒ $16x = 600$ ⇒ $x = \frac{600}{16}$ ⇒ $x = 37.5$ Now, $x\% \times 650 = 37.5\% \times 650= 243.75$ Again, $(x +20)\% \times 180$ = $(37.5 + 20)\% \times 180$ = $\frac{57.5}{100} \times 180$ = $103.5$ Percentage difference = $\frac{(243.75 - 103.50)}{103.50} \times 100$ = $\frac{140.25}{103.50} \times 100$ = $135.51 \approx 136\%$ Hence, the correct answer is 136%.
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Question : If decreasing 110 by $x\%$ gives the same result as increasing 50 by $x\%$, then $x\%$ of 650 is what percentage (correct to the nearest integer) is more than $(x-10)\%$ of 780?
Option 1: 12%
Option 2: 17%
Option 3: 14%
Option 4: 18%
Question : A's salary is 35% more than B's salary. How much percent is B's salary less than that of A's? (correct to the nearest integer)
Option 1: 17.5%
Option 2: 20%
Option 3: 35%
Option 4: 26%
Question : Two numbers are more than the third number by 20% and 80%, respectively. The first number is what percentage of the second number?
Option 1: 75%
Option 2: 50%
Option 3: 66.66%
Option 4: 150%
Question : A person takes 40 minutes more than his usual time when he covers a distance of 20 km at 5 km/hr. If he covers the same distance at 8 km/hr, he takes $x$ minutes less than the usual time. What is the value of $x$?
Option 1: 48
Option 2: 54
Option 3: 45
Option 4: 50
Question : In an entrance examination at different centres, a total of 25, 30, 40, 45, 60 and 100 students appeared. The pass percentages of the different centres are 20%, 30%, 35%, 40%, 50% and 75%, respectively. The pass percentage of the entrance examination is: (correct to the nearest integer)
Option 1: 59%
Option 2: 43%
Option 3: 53%
Option 4: 50%
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