(1)Raghu has some apple. He sold 40% more than he ate. If he sold 70 apples, how many did he ate?
(2)A man gives 10% of his money to his children and 20% of the remaining to trust.If he is still left Rs 9600, what did he originally have?
(3)A boy remains awake for 12 hours in a day. What percentage of time does he sleep?
(4)The percentage of total quantity represented by 90° sector in a pie chart is ?
(5)A income increase by 20% and then decrease by 20%, find the change in total percentage?
1.4 * ate = 70
ate = 50
what do you get for the other parts? If you get stuck, show how far you got. You must have at least some idea where to start, even if it is only defining a variable.
(1) To find the number of apples Raghu ate, we can start by setting up an equation. Let's assume he ate x apples. Since he sold 40% more than he ate, he sold 140% of x apples. We are given that he sold 70 apples, so we can write the equation:
140% of x = 70
To solve for x, first, convert 140% to decimal form by dividing by 100:
1.4x = 70
Next, isolate x by dividing both sides of the equation by 1.4:
x = 70 / 1.4 = 50
Therefore, Raghu ate 50 apples.
(2) Let's assume the man originally had x amount of money. He gives 10% of his money to his children, which leaves him with 90% remaining. He then gives 20% of the remaining money to a trust, leaving him with 80% of the remaining money. We are given that he is still left with Rs 9600, so we can set up the equation:
80% of 90% of x = 9600
To solve for x, first, convert the percentages to decimal form:
0.8 * 0.9 * x = 9600
Next, isolate x by dividing both sides of the equation by 0.72:
x = 9600 / 0.72 = 13333.33
Therefore, the man originally had Rs 13333.33.
(3) To find the percentage of time the boy sleeps, we can subtract the number of hours he remains awake (12 hours) from the total number of hours in a day (24 hours).
Percentage of time asleep = (12 / 24) * 100% = 50%
Therefore, the boy sleeps for 50% of the time.
(4) The percentage represented by a 90° sector in a pie chart can be found using the ratio of the angle measure of the sector to the total angle measure of the chart (360°).
Percentage = (Angle measure of sector / Total angle measure) * 100%
Percentage = (90° / 360°) * 100%
Percentage = 25%
Therefore, the 90° sector in the pie chart represents 25% of the total quantity.
(5) When the income increases by 20% and then decreases by 20%, the total percentage change can be calculated using the formula:
Total percentage change = (percentage change in first event + percentage change in second event) + [(percentage change in first event * percentage change in second event) / 100%]
In this case, the income increases by 20% and then decreases by 20%. Let's calculate the total percentage change:
Percentage change in first event = 20%
Percentage change in second event = -20%
Total percentage change = (20% + (-20%)) + [(20% * -20%) / 100%]
Total percentage change = 0% - 4%
Total percentage change = -4%
Therefore, the total percentage change after the income increase and decrease is -4%. This means that there was a 4% decrease in the income.