A student multiplied a number by \(\frac{3}{5}\) instead of \(\frac{5}{3}.\) What is the percentage error in the calculation?
Answer: D
Let the number be \(x.\)
Then, error \(= \frac{5}{3}x - \frac{3}{5}x = \frac{16}{15}x.\)
Error % \(= (\frac{16x}{15} \times \frac{3}{5x} \times 100)\)% \(= 64\)%
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In an election between two candidates, one got \(55\) % of the total valid votes, \(55\)% of the votes were invalid. If the total number of votes was \(7500\), the number of valid votes that the other candidate got, was:
Answer: A
Number of valid votes \(= 80\) % of \(7500 = 6000.\)
\(\therefore \) Valid votes polled by other candidate \(= 45\)% of \(6000\)
\(= (\frac{45}{100} \times 6000) = 2700.\)
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Three candidates contested an election and received \(1136, 7636\) and \(11628\) votes respectively. What percentage of the total votes did the winning candidate get?
Answer: A
Total number of votes polled \(= (1136 + 7636 + 11628) = 20400.\)
\(\therefore\) Requried percentage \(= (\frac{11628}{20400} \times 100)\)% \(= 57\)%
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Two tailors \(X\) and \(Y\) are paid a total of \(Rs. 550\) per week by their employer. If \(X\) is paid \(120\) % of the sum paid to \(Y\), how much is \(Y\) paid per week?
Answer: B
The sum paid to \(Y\) per week be \(Rs. Z.\)
Then, \(Z + 120\) % of \(Z = 550.\)
\(\Rightarrow Z + \frac{120}{100}Z =550\)
\(\Rightarrow \frac{11}{5}Z = 550\)
\(\Rightarrow Z = (\frac{550 \times 5}{11}) = 250.\)
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Priya went to the stationers and bought things worth \(Rs. 25\), out of which \(30\) paisa went on sales tax on taxable purchases. If the tax rate was \(6\) %, then what the cost of the tax free items?
Answer: C
The amount taxable purchases be \(Rs. x.\)
Then, \(6\) % of \(x = \frac{30}{100}\)
\(\Rightarrow x = (\frac{30}{100} \times \frac{100}{6}) = 5.\)
\(\therefore\) Cost tax free items \(= Rs. [25 - (5 + 0.30)] = Rs. 19.70\)
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Ayan buys good worth \(Rs. 6650.\) He gets a rebate of \(6\) % on it. After getting the rebate, he pays sales tax \(10\) %. Find the amount he will have to pay for the goods.
Answer: A
Rebate \(= 6\) % of \(Rs. 6650 = Rs. (\frac{6}{100} \times 6650) = Rs. 399.\)
Sales tax \(= 10\) % of \(Rs. (6650 - 399) = Rs. (\frac{10}{100} \times 6251) = Rs. 625.10\)
\(\therefore\) Final amount \(= Rs. (6251 + 625.10) = Rs. 6876.10.\)
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The population of a town increased from \(1,75,000\) to \(2,62,500 \) in a decade. The average percent increase of population per year is:
Answer: B
Increase in \(10\) years \(= (262500 - 175000) = 87500.\)
Increase % \(= (\frac{87500}{175000} \times 100)\) % \(= 50\) %
\(\therefore\) Required average \(= (\frac{50}{10})\) % \(= 5\) %
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