Exercise : Percentage - General Questions
✔ Percentage -
General Questions
31.
Out of total income, Mr. X spends 20% on house rent and 70% of the REST on household expenses. If he saves $3,600, find total income.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Let total income = 100.
2. Rent = 20. Remaining = 80.
3. Household expenses = \(70\% \text{ of } 80 = 56\).
4. Total spent = \(20 + 56 = 76\).
5. Savings = \(100 - 76 = 24\).
6. If 24 corresponds to 3600, then 100 corresponds to \(\frac{3600}{24} \times 100 = 15,000\).
2. Rent = 20. Remaining = 80.
3. Household expenses = \(70\% \text{ of } 80 = 56\).
4. Total spent = \(20 + 56 = 76\).
5. Savings = \(100 - 76 = 24\).
6. If 24 corresponds to 3600, then 100 corresponds to \(\frac{3600}{24} \times 100 = 15,000\).
32.
A solution of salt and water contains 5% salt. If 20 liters of water are evaporated, the salt becomes 15%. Find the original quantity of solution.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Let original quantity be \(x\) liters. Salt = \(0.05x\).
2. After evaporation, quantity = \(x - 20\). Salt = \(0.15(x - 20)\).
3. Since salt weight doesn't change: \(0.05x = 0.15x - 3\).
4. \(0.10x = 3\).
5. \(x = 30\) liters.
2. After evaporation, quantity = \(x - 20\). Salt = \(0.15(x - 20)\).
3. Since salt weight doesn't change: \(0.05x = 0.15x - 3\).
4. \(0.10x = 3\).
5. \(x = 30\) liters.
33.
The tax on a commodity is diminished by 20% and its consumption increases by 15%. Find the effect on revenue.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Revenue = Tax \(\times\) Consumption.
2. Let original Tax = 10, Consumption = 10. Revenue = 100.
3. New Tax = 8 (20% decrease). New Consumption = 11.5 (15% increase).
4. New Revenue = \(8 \times 11.5 = 92\).
5. Change = \(100 - 92 = 8\) decrease.
6. Alternatively: \(-20 + 15 + \frac{(-20 \times 15)}{100} = -5 - 3 = -8\%\).
2. Let original Tax = 10, Consumption = 10. Revenue = 100.
3. New Tax = 8 (20% decrease). New Consumption = 11.5 (15% increase).
4. New Revenue = \(8 \times 11.5 = 92\).
5. Change = \(100 - 92 = 8\) decrease.
6. Alternatively: \(-20 + 15 + \frac{(-20 \times 15)}{100} = -5 - 3 = -8\%\).
34.
If 20% of (A+B) = 50% of (A-B), find the ratio A:B.
View Answer
Answer: Option B
Explanation:
Explanation:
1. Write the equation: \(0.2(A+B) = 0.5(A-B)\).
2. Expand: \(0.2A + 0.2B = 0.5A - 0.5B\).
3. Rearrange terms: \(0.2B + 0.5B = 0.5A - 0.2A\).
4. \(0.7B = 0.3A\).
5. \(\frac{A}{B} = \frac{0.7}{0.3} = \frac{7}{3}\).
6. Ratio = 7 : 3.
2. Expand: \(0.2A + 0.2B = 0.5A - 0.5B\).
3. Rearrange terms: \(0.2B + 0.5B = 0.5A - 0.2A\).
4. \(0.7B = 0.3A\).
5. \(\frac{A}{B} = \frac{0.7}{0.3} = \frac{7}{3}\).
6. Ratio = 7 : 3.
35.
Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100kg of fresh fruit?
View Answer
Answer: Option B
Explanation:
Explanation:
1. In fresh fruit, pulp = \(100\% - 68\% = 32\%\).
2. Weight of pulp in 100kg fresh fruit = \(0.32 \times 100 = 32\) kg.
3. In dry fruit, pulp = \(100\% - 20\% = 80\%\).
4. This 32kg of pulp must equal 80% of the dry fruit weight (D).
5. \(0.80D = 32\).
6. \(D = \frac{32}{0.8} = 40\) kg.
2. Weight of pulp in 100kg fresh fruit = \(0.32 \times 100 = 32\) kg.
3. In dry fruit, pulp = \(100\% - 20\% = 80\%\).
4. This 32kg of pulp must equal 80% of the dry fruit weight (D).
5. \(0.80D = 32\).
6. \(D = \frac{32}{0.8} = 40\) kg.