Advertisements
Advertisements
प्रश्न
A solution of 9% acid is to be diluted by adding 3% acid solution to it. The resulting mixture is to be more than 5% but less than 7% acid. If there is 460 litres of the 9% solution, how many litres of 3% solution will have to be added?
उत्तर
Let x litres of 3% solution be added to 460 litres of 9%.
∴ Total amount of mixture = (460 + x) litres
Given that the acid contents in the resulting mixture is more than 5% but less than 7% acid.
∴ 5% of (460 + x) < `9/100 + 3/100 xx x < 7%` of (460 + x)
⇒ `5/100 (460 + x) < (4140 + 3x)/100 < 7/100 (460 + x)`
⇒ 5(460 + x) < 4140 + 3x < 3220 + 7x
⇒ 2300 + 5x < 4140 + 3x < 3220 + 7x
⇒ 2300 + 5x < 4140 + 3x and 4140 + 3x < 3220 + 7x
⇒ 5x – 3x < 4140 – 2300 and 3x – 7x < 3220 – 4140
⇒ 2x < 1840 and –4x < –920
⇒ `x < 1840/2` and 4x > 920
⇒ x < 920
∴ `x > 920/4` and x > 230
Hence the required amount of acid solution is more than 230 litres and less than 920 litres.
APPEARS IN
संबंधित प्रश्न
Solve: −4x > 30, when x ∈ Z
x + 5 > 4x − 10
\[\frac{3x - 2}{5} \leq \frac{4x - 3}{2}\]
−(x − 3) + 4 < 5 − 2x
\[\frac{2x - 3}{3x - 7} > 0\]
\[\frac{5x - 6}{x + 6} < 1\]
\[\frac{5x + 8}{4 - x} < 2\]
Solve each of the following system of equations in R.
1. x + 3 > 0, 2x < 14
Solve
\[\left| x + \frac{1}{3} \right| > \frac{8}{3}\]
Solve \[\frac{\left| x + 2 \right| - x}{x} < 2\]
Solve
\[\left| \frac{2x - 1}{x - 1} \right| > 2\]
Solve \[\frac{1}{\left| x \right| - 3} \leq \frac{1}{2}\]
Solve \[1 \leq \left| x - 2 \right| \leq 3\]
Mark the correct alternative in each of the following:
If − 3x\[+\]17\[< -\]13, then
Mark the correct alternative in each of the following:
Given that x, y and b are real numbers and x\[<\]y, b\[>\]0, then
Mark the correct alternative in each of the following:
If \[\left| x + 2 \right|\]\[\leq\]9, then
Solve the inequality, 3x – 5 < x + 7, when x is a whole number.
If x ≥ –3, then x + 5 ______ 2.
If p > 0 and q < 0, then p + q ______ p.
Solve for x, the inequality given below.
|x − 1| ≤ 5, |x| ≥ 2
The water acidity in a pool is considerd normal when the average pH reading of three daily measurements is between 8.2 and 8.5. If the first two pH readings are 8.48 and 8.35, find the range of pH value for the third reading that will result in the acidity level being normal.
State which of the following statement is True or False.
If x < –5 and x < –2, then x ∈ (–∞, –5)
If x < –5 and x > 2, then x ∈ (– 5, 2)
If x > – 5, then 4x ______ –20.
If x > y and z < 0, then – xz ______ – yz.
If p > 0 and q < 0, then p – q ______ p.
If |x + 2| > 5, then x ______ – 7 or x ______ 3.
If – 2x + 1 ≥ 9, then x ______ – 4.
