Question

13.
The ratio of milk and water in a mixture of 78 litres is 8:5. If this rat
becomes 3:4 on adding some water to the mixture, then the quantity
the water further added is_
(A) 34 litres (B) 24 litres (C) 22 litres (D) 28 litres​

Answer 1

Case:1

Let, the common multiple of the ratio be, 'x'

So, the amount of milk = (8*x)

                                      = 8x

The amount of water = (5*x)

                                     = 5x

By condition,

8x + 5x = 78

⇒ 13x = 78

⇒ x = 78/13

⇒ x = 6

So, the amount of milk = (8*6) liters

                                      = 48 liters

The amount of water = (6*5) liters

                                  = 30 liters

Case: 2

Since in both the cases the amount of milk remains same.

From the first case we get that the amount of milk is 48 litres and the amount of water is 30 litres.

As the amount of milk remains same so, the common multiple of the the second ratio we can get by dividing the amount milk by the second ratio of milk.

So, the common multiple of the second ratio is (48/3)

                                                                              = 16

So, the amount of water is present in the second case is (16*4) liters

                                                                                              = 64 liters

So, the amount of water is further added is = (64-30) liters

                                                                       = 34 liters

So, the answer is option (A) 34 liters.

Answer 2

The quantity of water added = 34 liters

Step-by-step explanation:

GIven:

Initial quantity of mixture of milk and water is 78 liters

Initial ratio of milk and water is 8:5

Here 8+5 = 13 units = 78 liters

1 unit = 6

Quantity of milk (initially) = $8\times 6$

                                         = 48 liters

Quantity of water(initially) = $5 \times 6$

                                           = 30 liters

Since the quantity of milk is same in both cases

3 units = 48 liters

1 unit = 16

So the quantity of water (final) = $16 \times 4$

                                                  = 64 liter

Quantity of water added = quantity of water(final) - quantity of water (initial)

                                        =  64 - 30

                                         = 34 liters