A solution made up of 40% alcohol by volume is mixed with 4 liters of solution that is 10% alcohol by volume. How much, in liters of the 40% alcohol solution is needed to make a mixture that is 25% alcohol by volume?

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A solution made up of 40% alcohol by volume is mixed with 4 liters of solution that is 10% alcohol by volume. How much, in liters of the 40% alcohol solution is needed to make a mixture that is 25% alcohol by volume?

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2025-01-04 04:42

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Shohan · Accepted Answer · 2024-12-14T13:31:11+06:00

$L e t, x l i t e r s o f 40 % a l c o h o l n e e d s t o b e a d d e d t o m a k e a m i x t u r e t h a t i s 25 % a l c o h o l .$

$A c c o r d i n g t o q u e s t i o n,$

$40 % o f x + 10 % o f 4 = 25 % o f (x + 4)$

$= \frac{40 x}{100} + \frac{10 \times 4}{100} = \frac{25 (x + 4)}{100}$

= $40 x + 40 = 25 x + 100 [M u l t i p l y i n g b o t h s i d e s b y 100]$

= $40 x - 25 x = 100 - 40$

= $15 x = 60$

$∴ x = \frac{60}{15} = 4 (a n s w e r)$