The square of a positive number is 20 times greater than the number itself. The square of the number is…. ?
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Solution
X2 -x = 20x
⇒x2 = 21x
⇒ x = 21
Required Answer = 21
∴ 212 = 441
The salary of A is 20% lower than B’s salary and the salary of C is 50% greater than A’s salary. By how much percent the salary of B is less than salary of C?
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Solution
Let the salary of B be 100
B100 ⇒ A80 ⇒ C120
∴ Required value
\(\frac{20}{120}\) = 16.67%
A milkman has a mixture of milk in which the ratio of milk and water is 5:3. He sells 40 litres of mixture; then he adds 15 liters of pure water. Now the ratio of milk and water is 5:4. What is the new proportion of mixture A in the solution?
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Solution
Milk Water Total Ratio 5 3 Quantity 5x 3x 8x Quantity Remaining 5x - 25 3x - 15 = 3x
∴ \(\frac{5x - 25}{3x}\) = 5⁄4 = 20x -100 = 15x
⇒ 5x = 100 ⇒ x = 20
Initial Quantity = 8x = 160 Liters
Therefore, the new quantity = 160 - 25 = 135
In what ratio should water and wine be mixed so that after selling the mixture at a cost price, a profit of 33.33% is made?
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Solution
33.33% profit means, the mixture contains 1 part water and 3 parts pure wine. So the required ratio water and wine is 1 : 3
The average score of a batsman after 48 innings is 48 and in the 49th inning the batsman scores 97 runs. In the 50th inning, what is the minimum number of runs that the batsman should score so that his average score increases by 2, over the average of the 49 innings?
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Solution
Total score in 49 inning (48 x 48) + 97 = 2401
Average score after 49 innings = \(\frac{2401}{49}\) = 49
New average after 50 innings = 49 + 2 = 51
Runs in 50th inning = (51 x 50) - 2401 = 149
When you reverse the digits of number 13, the number increases by 18. How many other two digit number increase by 18 when their digits are reversed?
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Solution
Let the number be 10 x + y
After renersing the digits, number is 10y + x
Given that (10y + x) - (10x + y) = 18
9 (y-x) = 18 ⇒ (y-x) = 2
Possible pairs of (x, y) are (1,3) (2, 4) (3, 5) (4,6) (5, 7) (6, 8) (7, 9)
Apart from 13, '6' other numbers can be formed
A dealer buy fruits at $100, $80 and $60 per kg. He mixes them in the ratio 3:4:5 by weight and sells them at profit of 5%. At what price per kg does he sell the fruits?
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Solution
He mixes of 3kg of $100 per kg 4 kg of $80 per kg and 5 kg of $60 per kg
Total Q + y = 3 + + 4 + 5 = 12 kg
Total Cost price = 300 + 320 + 300 = 920/-
% profit = 5%
Total SP =920 + 46 = 966
SP per unit = \(\frac{966}{12}\) = 80.50/-
I have one dollar coin, fifty cents coins and twenty five cents coins. The number of coins is in the ratio 5 : 6 : 8. If the total amount with me is $210; what are the number of one dollar coins?
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Solution
Ration value of coins 1: 0.5: 0.25
Ratio of no of coins 5: 6 : 8
No of coins 5x: 6x: 8x
Value of coins in $ 5x: 3x: 2x
⇒ 5x + 3x + 2x = 210
X = 21
No of 1 Dollar coins = 21 x 5 = 105
The length, breadth and height of a room are in the ratio 3 : 2 : 1. If breadth and height are halved while the length is doubled, the total area of the four walls will get decreased by what percentage?
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Solution
Let the length be 3; breadth be 2 and heights be 1 units.
∴ Area of 4 walls = 2h (1 + b)
= 2 x 1(3+ 2) = 10
New length breadth height
6 1 0.5
New area = 2h (1 + b)
= 2 x 0.5(6+1) = 7
Decrease in area =\(\frac{10-7}{10}=\frac{3}{10}=30\)%
One bacteria splits into eight bacteria for the next generation. But due to the environment hazards, only 50% of the bacteria survive and split into 8 for the next generation. If in the seventh generation number is 4096 million what is the number in the first generation?
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Solution
Let us consider 2x as the initial quantity of bacteria in the first generation. Out of which only Ix will survive and split into 8x. For the second generation out of which, only 4x will survive and split into 32x for the third generation. Out of which only 16x will survive and split into 128x for the fourth generation.
Thus the increase is 1,4,8, 16, 64 .In G.P. with the common multiple 4
∴ Quantity in the seventh generation
∴ 4096 = x = (4)7-1
= X = 46 = x = 4096
∴ x = 1 million
Original number of the first generation was 2x
i.e. 2 million.