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?
Answers
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.
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