Basic Numeracy/Quantitative Aptitude

Detailed Solution

29. c: Let x and y be the weights, in grams, of sterling silver and of the 90% alloy to make the 500 grams at 91%. Hence x + y =500
The number of grams of pure silver in x plus the number of grams of pure silver in y is equal to the number of grams of pure silver in the 500 grams. The pure silver is given in percentage forms. Hence 92.5% x + 90% y = 91% 500
Substitute y by 500 - x in the last equation to write 92.5% x + 90% (500 - x) = 91% 500 Simplify and solve 92.5 x + 45000 - 90 x = 45500
x = 200 grams.
200 grams of Sterling Silver is needed to make the 91% alloy.

30. a: Let x be the weights, in Kilograms, of pure water to be added. Let y be the weight, in Kilograms, of the 10% solution. Hence x + 100 = y
Let us now express the fact that the amount of salt in the pure water (which 0) plus the amount of salt in the 30% solution is equal to the amount of salt in the final saline solution at 10%.
0 + 30% 100 = 10% y
Substitute y by x + 100 in the last equation and solve.
30% 100 = 10% (x + 100)
Solve for x.
x = 200 Kilograms.

31. c: The amount of the final mixture is given by 50 ml + 30 ml = 80 ml
The amount of alcohol is equal to the amount of alcohol in pure water ( which is 0) plus the amount of alcohol in the 30% solution. Let x be the percentage of alcohol in the final solution. Hence 0 + 30% 50 ml = x (80)
Solve for x
x = 0.1817 = 18.75%

32. c: Let us first find the amount of alcohol in the 10% solution of 200 ml.
200 * 10% = 20 ml
The amount of alcohol in the x ml of 25% solution is given by 25% x = 0.25 x
The total amount of alcohol in the final solution is given by 20 + 0.25 x
The ratio of alcohol in the final solution to the total amount of the solution is given by [ ( 20 + 0.25 x ) / (x + 200)]
If x becomes very large in the above formula for the ratio, then the ratio becomes close to 0.25 or 25% (The above function is a rational function and 0.25 is its horizontal asymptote). This means that if you increase the amount x of the 25% solution, this will dominate and the final solution will be very close to a 25% solution.
To have a percentage of 15%, we need to have [ ( 20 + 0.25 x ) / (x + 200)] = 15% = 0.15
Solve the above equation for x
20 + 0.25 x = 0.15 * (x + 200)
x = 300 ml

33.

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