Question

Cement mortar was being prepared by mixing cement to sand in the ratio of 1:6 by volume. In a cement mortar of 42 units of volume, how much more cement needs to be added to enrich the mortar in the ratio 2:9?

Answer 1

Given that:

• Cement mortar was being prepared by mixing cement to sand in the ratio of 1 : 6 by volume.
• In a cement mortar of 42 units of volume.

To Find:

• How much more cement needs to be added to enrich the mortar in the ratio 2 : 9?

Let us assume:

• Initially cement and sand be x units and 6x units respectively.

According to the question.

↣ x + 6x = 42

↣ 7x = 42

↣ 7x = 7(6)

Cancelling 6.

↣ x = 6

Cement = x = 6 units

Sand = 6x = 6(6) = 36 units

Let us suppose:

• S units more cement added and the ratio of cement to sand became 2 : 9.

New equation,

↣ (6 + S) : 36 = 2 : 9

↣ (6 + S) / 36 = 2 / 9

Cross multiplication.

↣ 9 (6 + S) = 2 (36)

↣ 54 + 9S = 72

↣ 9S = 72 - 54

↣ 9S = 18

↣ 9S = 9(2)

↣ S = 2

Hence,

• 2 units more cement needs to be added to enrich the mortar in the ratio 2 : 9.

Answer 2

Given :-

Cement mortar was being prepared by mixing cement to sand in the ratio of 1:6 by volume. In a cement mortar of 42 units of volume

To Find :-

How much more cement needs to be added to enrich the mortar in the ratio 2:9?

Solution :-

Total part = 6 + 1 = 7

Volume of cement = 42/(6 + 1)

Volume of cement = 42/7

Volume of cement = 6 units

Now

Volume of sand = 6 × 6

Volume of sand = 36 units

Volume of cement = 6 units

Let the cement to be added be a

6 + a/36 = 2 : 9

6 + a/36 = 2/9

9(6 + a) = 2(36)

54 + 9a = 72

9a = 72 - 54

9a = 18

a = 18/9

a = 2

Henceforth, Two units of more cement should be added to get ratio as 2:9