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Ncert Solutions Maths class 11th Maths Class 11th Linear Inequalities

64. 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?

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Payal Gupta | Contributor-Level 10

4 months ago

64. Let x litre of water is required to added.

Then, total mixture =(x+1125) litre.

As, 0 % of acid is contained in pure mater (neutral).

$∴$ 0% of x + 45% of 1125% > 25% of (x+1125)

$\Rightarrow \frac{0 \times x}{100} + \frac{45}{100} \times 1125 > \frac{25}{100} (x + 1125)$ (multiplying by 100 throughout)

$\Rightarrow$

$\Rightarrow \frac{1125 \cdot (45 - 25)}{25} > \frac{25 x}{25}$ (dividing by 25 throughout)

$\Rightarrow \frac{1125 \times 20}{25} > x$

$\Rightarrow 900 > x$ ……(1)

And 0% of x+ 45% of 1125<30 of (x+1125)

$\Rightarrow \frac{0}{100} \times x + \frac{45}{100} \times 1125 < \frac{30}{100} (x + 1125)$

$\Rightarrow 45 \times 1125 < 30 (x + 1125)$ {multiplying by 100 throughout)

$\Rightarrow 45 \times 1125 < 30 x + 30 \times 1125$

$\Rightarrow$ 45 × 1125 – 30 × 1125 < 30x

$\Rightarrow \frac{1125 (45 - 30)}{30} < \frac{30 x}{30}$ {dividing by 30 throughout}

$\Rightarrow \frac{1125 \times 15}{30} < x$

$\Rightarrow$ 562.5

From (1) and (2),

562.5

Thus, the water to be added has to be more than 562.5 litre but less than 900 litres.

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64. 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?

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