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Question 1 / 2
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1
Two individuals, A and B, entered into a partnership with $700 and $600 respectively. A withdraws 2/7 of his stock after 3 months and then puts back 3/5 of what he had withdrawn after another 3 months. If the total profit at the end of the year is $726, what amount should A receive?
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Solution: Step 1: Calculate Y's investment for 12 months = $600 * 12 = $7200 Step 2: Calculate A's investment: For first 3 months = $700 * 3 = $2100 For next 3 months = ($700 - 2/7 * $700) * 3 = $500 * 3 = $1500 A withdraws 2/7 * $700 = $200 and then invests back 3/5 * $200 = $120 For the remaining 6 months = ($500 + $120) * 6 = $620 * 6 = $3720 Step 3: Total A's investment = $2100 + $1500 + $3720 = $7320 Step 4: Ratio of their investments = $7320 : $7200 Step 5: A's share of profit = ($7320 / ($7320 + $7200)) * $726 = $366
2
Person A started a business with Rs. 21,000. Person B joined later with Rs. 42,000. If the year-end profits are divided in a 3:1 ratio, how long did Person B join for?
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Solution: Step 1: Let's assume Person B joined for 't' months. Step 2: Person A's investment for the whole year = 21,000 * 12. Step 3: Person B's investment = 42,000 * t. Step 4: The profit ratio is given as 3:1, so we can set up the equation: (21,000 * 12) / (42,000 * t) = 3 / 1 Step 5: Solving for t: 252,000 / (42,000 * t) = 3 252,000 = 126,000 * t t = 252,000 / 126,000 t = 2 Step 6: Therefore, Person B joined for 2 months.
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