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%
Correct Answer: 14%
Solution : On decreasing 110 by $x\%$ as $110(1 - \frac{x}{100})$ and the increase of 50 by $x\%$ as $50(1 + \frac{x}{100})$. According to the question, $⇒110(1 - \frac{x}{100}) = 50(1 + \frac{x}{100})$ $⇒1100-11x=500+5x$ $⇒16x=600$ $⇒x=\frac{75}{2}$ $⇒x=37.5$% Next, we calculate $x\%$ of 650. So, 650 × $\frac{37.5}{100}$ = 243.75 Then,$(x-10)\%$ of 780. So, 780 × $\frac{27.5}{100}$ = 214.5 The required percentage = $\frac{243.75-214.5}{214.5}$ × 100 = 13.63% ≈ 14% Hence, the correct answer is 14%
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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 more than ($x$ + 20)% of 180? (correct to the nearest integer)
Option 1: 136%
Option 2: 90%
Option 3: 154%
Option 4: 80%
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 : Rice is now being sold at INR 29 per kg. During the last month, its cost was INR 25 per kg. By how much percentage should a family reduce its consumption, to keep the expenditure the same as before? (correct to the nearest integer)
Option 1: 14%
Option 2: 13%
Option 3: 15%
Option 4: 12%
Question : If the number 8764x5 is divisible by 9, then find the least possible value of x where x is a two-digit number.
Option 1: 15
Option 2: 06
Option 3: 14
Option 4: 18
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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