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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 are 460 liters of the 9% solution, how many liters of the 3% solution will have to be added?

0 2 Views | Posted 3 months ago
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    Answered by

    Payal Gupta | Contributor-Level 10

    3 months ago

    This is a short answer type question as classified in NCERT Exemplar

    L e t     x     l i t r e s     o f     3 %     s o l u t i o n     b e     a d d e d     t o     4 6 0     l i t r e s     o f     9 % . ∴     T o t a l     a m o u n t     o f     m i x t u r e = ( 4 6 0 + x ) l i t r e s G i v e n     t h a t     t h e     a c i d     c o n t e n t s     i n     t h e     r e s u l t i n g     m i x t u r e     i s     m o r e     t h a n     5 %     b u t     l e s s     t h a n     7 %     a c i d . ∴     5 %     o f     ( 4 6 0 + x ) < 4 6 0 × 9 1 0 0 + 3 1 0 0 × x < 7 %     o f     ( 4 6 0 + x ) ⇒ 5 1 0 0 ( 4 6 0 + x ) < 4 1 4 0 + 3 x 1 0 0 < 7 1 0 0 ( 4 6 0 + x ) ⇒                 5 ( 4 6 0 + x ) < 4 1 4 0 + 3 x < 7 ( 4 6 0 + x ) ⇒                     2 3 0 0 + 5 x < 4 1 4 0 + 3 x < 3 2 2 0 + 7 x ⇒                     2 3 0 0 + 5 x < 4 1 4 0 + 3 x     a n d     4 1 4 0 + 3 x < 3 2 2 0 + 7 x ⇒                               5 x − 3 x < 4 1 4 0 − 2 3 0 0     a n d     3 x − 7 x < 3 2 2 0 − 4 1 4 0 ⇒                                                   2 x < 1 8 4 0     a n d     − 4 x < − 9 2 0 ⇒                                                         x < 1 8 4 0 2     a n d     4 x > 9 2 0 ⇒                                                         x < 9 2 0     a n d     x > 9 2 0 4       ∴ x > 2 3 0 H e n c e ,     t h e     r e q u i r e d     a m o u n t     o f     a c i d     s o l u t i o n     i s     m o r e     t h a n     2 3 0     l i t r e s     a n d     l e s s     t h a n     9 2 0     l i t r e s .

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