Two numbers \(A\) and \(B\) are such that the sum of 5 % of \(A\) and 4 % of \(B \) is two-third of the sum of 6 % of \(A\) and 8 % of \(B. \) Find the ratio of \(A:B\)
Answer: D
5 % of \(A\) + 4% of \(B\) \(= \frac{2}{3}\) (6% of \(A + 8\)% of \(B\))
\(\Rightarrow \frac{5}{100}A + \frac{4}{100}B = \frac{2}{3}(\frac{6}{100}A + \frac{8}{100}B)\)
\(\Rightarrow \frac{1}{20}A + \frac{1}{25}B = \frac{1}{25}A + \frac{4}{75}B\)
\(\Rightarrow (\frac{1}{20} - \frac{1}{25})A = (\frac{4}{75} - \frac{1}{25})B\)
\(\Rightarrow \frac{1}{100}A = \frac{1}{75}B\)
\(\frac{A}{B} = \frac{100}{75} = \frac{4}{3}\)
\(\therefore Required ratio = 4: 3\)
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A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percentage of his total score did he make by running between the wickets?
Answer: B
Number of runs made by running \(= 110 - (3 \times 4 + 8 \times 6) \)
\(= 100 - (60) \)
\(= 50.\)
\(\therefore\) Required percentage \(= (\frac{50}{110} \times 100)\)% \(= 45\frac{5}{11}\)%
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A man spends 59% of his income and saves the rest. What percentage of his expenditure does he save?
Answer: D
Total income of man = Rs. \(100x\)
Amount spend \(= \frac{59}{100} \times 100x = 59x\) (Rs.)
\(\Rightarrow \) Money saved \(= 100x - 59x = 41x\)
\(\therefore\) Percentage of his expenditure that he saves \(= \frac{41x}{59x} \times 100 = 69.49 \) %
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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 marked price of a shirt is Rs 1280. If the shirt is being sold for Rs 900, then
what is the discount percentage?
Answer: C
Marked price \(= Rs. 1280\)
Selling price \(= Rs. 900\)
⇒ Discount % \(= \frac{1280-900}{1280} \times 100 \)
\(= \frac{380}{12.8} \)
\(= 29.68\)
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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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If 30% of A is added to 40% of B, the answar is 80% of B. What percentage of A is B?
Answer: D
It is given that
0.3 A + 0.4 B = 0.8 B
0.3 A = 0.4 B
A = 4/3 B
B = 3/4 A
heance B is 75 % of A
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A man spends 75% of his income. His income increases by 20% and his
expenditure also increases by 10%. The percentage of increase in his savings is
Answer: C
The income of person be Rs \(y\)
So his expenditure be 75% of income which is \(= 0.75y\)
Saving \(= y- 0.75y = 0.25y\)
Now after increment of 20 % in income the new income becomes \(= 1.2y\)
Given that bew expenditure is 10% more than previous one.So , new expenditure is \(= 1.1 \times 0.75y = 0.825y\)
New savings \(= 1.2y – 0.825y = 0.375y\)
Percentage increase in savings \(= \frac{0.375y-0.25y}{0.25y} \times 100 = 50%\)
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If 20 % of \(a = b\), then \(b\) % of 20 is the same as:
Answer: A
20 % of \(a = b \Rightarrow \frac{20}{100}a = b.\)
\(\therefore b\) % of \(20 = (\frac{b}{100} \times 20) = (\frac{20}{100}a \times \frac{1}{100} \times 20) = \frac{4}{100}a = 4\)% of \(a\)
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