Three bottles of equal capacity containing mixture of milk and water in ratio 2 : 5, 3 : 4 and 4 : 5 respectively. These three bottles are emptied into a large bottle. What will be the ratio of milk and water respectively in the large bottle?
Three bottles of equal capacity containing mixture of milk and water in ratio 2 : 5, 3 : 4 and 4 : 5 respectively. These three bottles are emptied into a large bottle. What will be the ratio of milk and water respectively in the large bottle?
1). 73 : 106
2). 73 : 116
3). 73 : 113
4). 73 : 189
1 answers
Let the capacity be z litres
For bottle 1, 2 : 5 implies that milk is 2a and water is 5a
⇒ 2a + 5a = z
⇒ a = z/7 …..(i)
For bottle 2, 3 : 4 implies that milk is 3b and water is 4b
⇒ 3b + 4b = z
⇒ b = z/7 …..(ii)
For bottle 1, 4 : 5 implies that milk is 4c and water is 5c
⇒ 4c + 5c = z
⇒ c = z/9 …..(iii)
Total milk is = 2a + 3b + 4c Using (i), (ii) and (iii)
⇒ milk = 2 × z/7 + 3 × z/7 + 4 × z/9
Total water is 5a + 4b + 5c
⇒ water = 5 × z/7 + 4 × z/7 + 5 × z/9
Ratio of milk and water is given as
⇒ (2 × z/7 + 3 × z/7 + 4 × z/9) / ( 5 × z/7 + 4 × z/7 + 5 × z/9)
⇒ 73/116
∴ ratio is 73 : 116