Q13 of 65 Page 132

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

45% of solution of acid = 1125 litres


Let x litres of water is added


Resulting mixture = x + 1125 litres


The resulting mixture has to be more than 25% but less than 30% acid content.


Amount of acid in resulting mixture = 45% of 1125 litres.


∴ 45% of 1125 < 30% of (x + 1125) and 45% of 1125 > 25% of (x + 1125)


45% of 1125 < 30% of (x + 1125)



⇒ 45 × 1125 < 30x + 30 × 1125


⇒ (45 – 30) × 1125 < 30x


⇒ 15 × 1125 < 30x


⇒ x > 562.5 ………..(I)


45% of 1125 > 25% of (x + 1125)



⇒ 45 × 1125 > 25x + 25 × 1125


⇒ (45 – 25) × 1125 > 25x


⇒ 25x < 20 × 1125


⇒ x < 900 …..(II)


∴ 562.5 < x < 900


Number of litres of water that has to be added will have to be more than 562.5 litres but less tan 900 litres.


More from this chapter

All 65 →
10

Solve the inequalities and represent the solution graphically on number line: 5(2x – 7) – 3(2x + 3) ≤ 0, 2x + 19 ≤ 6x + 47

 11

A solution is to be kept between 68° F and 77° F. What is the range in temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by

12

A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8% solution, how many litres of the 2% solution will have to be added?

 14

IQ of a person is given by the formula

,


Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.