Question: In what ratio should a mixture of 20% alcohol strength be mixed with a mixture of 60% alcohol strength to get a mixture of 50% alcohol strength?

Solution:
Let the ratio be 1 : x
Then according to the question
⇒ 20 × 1 + 60x = (1 + x) 50
⇒ 20 + 60x = 50 + 50x
⇒ 60x - 50x = 50 - 20
⇒ 10x = 30
⇒ x = 3

∴ the ratio is 1 : 3

প্রশ্ন: x2 - y2 = 15 এবং x + y = 5 হলে, 8xy(x2 + y2) = ?

সমাধান:

দেওয়া আছে,

x2 - y2 = 15

বা, (x + y)(x - y) = 15

বা, 5(x - y) = 15

∴ x - y = 3

প্রদত্ত রাশি,

8xy(x2 + y2)

= 4xy.2(x2 + y2)

= {(x + y)2 - (x - y)2}{(x + y)2 + (x - y)2}

= (52 - 32)(52 + 32)

= 16 × 34

= 544

Question: In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is-

Solution:
Quantity of milk = 60 × (2/3) litres = 40 litres.
Quantity of water in it = (60 -  40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then,
milk : water = 40/(20 + x)
Now,
40/(20 + x) = 1/2
⇒ 20 + x = 80
∴ x = 60.
Quantity of water to be added = 60 litres.