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Ans 1.)The average (arithmetic mean) of the 5 numbers 28, x, 42, 78 and 104 is 62.
Therefore, the sum of these 5 numbers is 62 * 5 = 310
i.e., 28 + x + 42 + 78 + 104 = 310
Hence, x = 310 - 252 = 58.
The average of 128, 255, 511, 1023 and x = = 395
Ans 2)The correct choice is (D) and the correct answer is 37 years 6 months.
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $400.
Therefore, the Simple Interest earned = 400 - 100 = $300.
We know that Simple Interest =
Substituting the values in the above equation we get 300 =
Or 8n = 300
Or n = 37.5 years.
Ans 3)Let there be 1 litre of the solution after mixing 20% methyl alcohol and 50% methyl alcohol..
If the concentration of methyl alcohol in it is 40%, then 0.4 litres of the resultant mixture is methyl alcohol.
Let x litres of the solution containing 20% methyl alcohol be mixed with (1 - x) litres of the solution containing 50% methyl alcohol to get 1 litre of the solution containing 40% methyl alcohol.
X litres of 20% methyl alcohol solution will contain 20% of x = 0.2x litres of methyl alcohol in it.
(1 - x) litres of 50% methyl alcohol solution will contain 50% of (1- x) = 0.5(1 - x) litres of methyl alcohol.
The sum of these quantities of methyl alcohols added up to the total of 0.4 litres in the resultant mixture.
Therefore, 0.2x + 0.5(1 - x) = 0.4 litres
0.2x + 0.5 - 0.5x = 0.4
0.5 - 0.4 = 0.5x - 0.2x
x = litres
And 1 - x = 1 - litres.
So, the two solutions are mixed in the ratio of 1 : 2.
Ans 4)A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point.
That is, if they are not parallel lines. i.e., the two lines should have different slopes.
ax + by + c = 0 and dx + ey + g = 0 will not represent two parallel lines if their slopes are different.
i.e., when
In the question given above, a = 3, b = 4, d = k and e = 12.
Therefore, or 'k' should not be equal 9 for the pair of equations to have a unique solution.
In other words, when k = 9, the system of equation will not have any solution as the two lines represented by the equations will be parallel lines.
Ans 5) The cost price of 1 apple = th of a dollar or $0.10.
As Sam wishes to make a profit of 25%, his selling price per apple will be 0.10 + 25% of 0.10 = $0.125.
If the selling price of 1 apple is $0.125, then the selling price of a dozen apples = 12 * 0.125
= $1.5
Note:The level of questions here are a bit difficult here.But you can expect these questins with minimum level of difficulty than this.
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