Percentage SET: Q26-Q30
Solution: 2
Let the total marks be X
Then, marks obtained by student 1 = 0.2X
Since, student 1 fails by 30 marks after getting 20% marks
∴ According to student1, Passing marks = 0.2X + 30
Similarly, Marks obtained by student 2 = 0.32X
And according to student 2, passing marks = 0.32X - 42;
Equating eq. 1 and 2, we get
0.2X + 30 = 0.32X - 42
0.12X = 72
X = 72/0.12 = 600
⇒ X = 600
∴ Passing marks = (0.2 × 600) + 30 = 150
Passing marks % =
Solution: 3
Given:
Initially tank filled with petrol A.
When tank half empty, tank filled with B rest of the way.
When this mix is emptied to half the total tank, again A is added.
Calculation:
Let the capacity of the tank be 100 litres.
Initially: A type Petrol = 100 Litres.
After first operation:
A type petrol left = [(100/2)] = 50 Litres
B type petrol = 50 Litres
After second operation:
A type petrol = (50/2) + 50 = 75 Litres;
B type petrol = [50/2] = 25 Litres.
After third operation:
A type petrol = (75/2) = 37.5 Litres;
B type petrol= [(25/2) + 50)] = 62.5 Litres.
∴ Required percentage= 37.5%
Alternate Method
A = 1 initially (Tank filled with A fully)
After first operation = A1 = 1/2 of total (A used till half the tank and B added half the tank)
After second operation = A = 1/2 of A1 + 1/2 of tank (1/2 of mixture goes out + half tank filled with A)
⇒ 1/4 × A + 1/2 × A = 3/4 × A
After third operation = A = 3A/4 × 1/2 (half the mixture used + B added in rest of the tank)
Total A left = 3A/8
Percentage of A remaining = 3/8 × 100 = 37.5%
∴ Required percentage= 37.5%
28. At an election between two candidates, the candidate who got 66% of the votes casted won by 3072 votes. Find the total number of the voters on the voting list if 80% people casted their vote and there were no invalid votes.
Solution: 2
The winning candidate gets 66 % of the votes cast and the losing candidate gets (100 - 66 = 34%) of the votes casted.
Thus , the gap between the two is (66 - 34 = 32%) of the votes cast = 3072 votes .
Thus, the total votes cast =
Since, this is 80 % of the total number of voters on the voting list,
Hence, the total number of voters on the voting list =
Solution: 4
Given,
Weight of dry grapes = 300 kg
∵ Dry grapes contain 20% water,
∴ Weight of water in dry grapes = 0.20 × 300 kg = 60 kg
∴ Weight of the pulp of the grapes = 300 kg – 60 kg = 240 kg
Again,
Fresh graphs contain 75% water
∴ Amount of pulp in fresh grapes = 25%
∵Weight of the pulp of the grapes will be same in both fresh and dry grapes
∴ 0.25 × Weight of fresh grapes = 240 kg
⇒ Weight of fresh grapes = 240/0.25 = 960 kgSolution: 1
ratio of salary in july and june
⇒5/2 : 9/4
⇒10/4 : 9/4
⇒10 : 9
Let salary of june be 9m.
Then percentage increase from june to july = (10m – 9m) × 100/9m
= 100m/9m
= 100/9 %
=
Also,
Percentage of salary of June was less than the of July = (10m – 9m) × 100/10m
= 100m/10m
= 100/10
= 10 %
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