Percentage SET: Q21-Q25
Solution: 2
Shortcut Trick
Income = Saving × (100/(100 – R1)) × (100/(100 – R1)) × (100/(100 – R1))
⇒ 1224 × (100/90) × (100/80) × (100/85)
⇒ Rs. 2000
∴ Total sum is Rs. 2000
Alternate Method
Let’s assume that initially Manoj has Rs.X
First Manoj gives 10% of his money to his eldest son
⇒ money given to the eldest son = 0.1X
⇒ Remaining money = X – 0.1 X = 0.9 X
Then, he gives 20% of the remaining money to his youngest son
⇒ money given to the youngest son = 0.9X × 0.20 = 0.18X
⇒ Remaining money = 0.9X – 0.18X = 0.72X
Then, he gives 15% of the remaining money to a school for poor boys
⇒ money given to school for poor boys = 0.72X × 0.15 = 0.108X
⇒ Remaining money = 0.72X – 0.108X = 0.612X
Given finally remaining money = 1224
⇒ 0.612X = 1224
⇒ X = 2000
∴ The total sum is = Rs. 2000
Solution: 2
Dhaval got 300 marks.
As per the given information, Charmi got 20% more marks than Dhaval
∴ Marks obtained by Charmi = 300 + 20% of 300
⇒ Marks obtained by Charmi = 300 + 60 = 360
As per the given information, Bunny got 25% less marks then Charmi
∴ Marks obtained by Bunny = 360 – 25% of 360
⇒ Marks obtained by Bunny = 360 – 90 = 270
As per the given information, Aditi got 10% marks more than Bunny
∴ Marks obtained by Aditi = 270 + 10% of 270
⇒ Marks obtained by Aditi = 270 + 27 = 297Solution: 3
Given:
If entry fee reduced by 35% then,
Number of people increased by 40%
Calculation:
Let the original entry fee be ‘a’ and
The number of people initially coming to the park be ‘b’.
⇒ Total income = a × b = ab
Now, reducing the entry fee by 35% in a park,
the number of people coming to the park increased by 40%
⇒ New entry fee = a – (35% of a) = 0.65a
⇒ New number of people = b + (40% of b) = 1.4b
⇒ New total income = 0.65a × 1.4b = 0.91ab
⇒ Decrease in income = ab – 0.91ab = 0.09ab
% decrease in income
∴ % decrease in income is 9%
Alternate Method
Let the fee per person be 100x and
The total number of people who are coming to the park initial is 100y
Total income = 100x × 100y = 10000xy f
According to the question
New per person fee = 100x × (100 - 35)/100 = 65x
New total number of person = 100y × (100 + 40)/100 = 140y
Total income = 65x × 140y = 9100xy
Decrease in income = 10000xy - 9100xy = 900xy
Decrease% = (900xy/10000xy) × 100 = 9%
∴ Decrease% in income is 9%
Solution: 1
Let the strength of school in 2000 be ‘a’.
Given, the strength of a school increases and decreases in every alternate year by 10%.
⇒ Strength of school in 2001 = a + 10% of a
⇒ Strength of school in 2001 = 1.1a
Strength of school in 2002 = 1.1a – 10% of 1.1a
⇒ Strength of school in 2002 = 0.99a
Strength of school in 2003 = 0.99a + 10% of 0.99a
⇒ Strength of school in 2003 = 1.089a
% increase in strength
⇒ % increase in strength
⇒ % increase in strength = 8.9%
Concept used:
a% = a/100
Where,
100 → Initial value
a → Changes
Calculations:
10% = 10/100 = 1/10
Let strength of school in 2000 be 10x
| Year | Strength |
| 2000 | 10x |
| 2001 | 10x × (110/100) = 11x |
| 2002 | 11x × 90/100 = 9.9x |
| 2003 | 9.9x × (110/100) = 10.89x |
Changes from 2000 to 2003 = 10.89x – 10x = 0.89x
Increase% = (0.89x/10x) × 100 = 8.9%
∴ Increase% in strength is 8.9%
Solution: 1
Let the total number of votes be v.
Given, 20% of votes were not polled.
∴ Total number of votes polled = v – 20% of v = 0.8v
Now, Ram received 40% of total votes polled
Votes received by Ram = 40% of 0.8v = 0.32v
Bhanu received 60% of total votes polled.
Votes received by Bhanu = 60% of 0.8v = 0.48v
Given, Bhanu won by 1600 votes.
∴ 0.48v – 0.32v = 1600
⇒ 0.16v = 1600
⇒ v = 10000
Votes received by Bhanu = 0.48 × 10000 = 4800
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