Question

Mortar consists of 50% sand, 10% lime and the rest of it is cement. Find the quantity of cement in 400 kg of the mortar.

Answer 1

Hint: We will first combine the percentage of sand and lime in the mortar. Then subtract the (resultant from 100 to get the percentage of cement in the mortal. After that we will multiply that percent by 400 and divide the resultant by 100 to get the quantity of cement in the mortar.

Complete step-by-step answer:
We are given that the mortar consists of 50% sand and 10% lime.
Total of combined sand and limes is (50 + 10)% that is 60%.
Hence, the percentage of cement in the mortar is (100 – 60)% that is equivalent to 40%.
Since, we have 40% of cement in mortar.
Hence, in 400 kg of mortal we will have:-
$\dfrac{{40}}{{100}} \times 400kg$ that is equivalent to $40 \times 4kg = 160kg$.
Hence, we have 160 kg of cement in 400 kg or mortar.

Note: The students may use an alternate way as follows to solve the same question:-
Firstly find the quantity of sand in 400 kg mortar:
Quantity of sand in 400 kg mortar is $\dfrac{{50}}{{100}} \times 400kg$ that is equal to $50 \times 4kg = 200kg$ ……(1)
Quantity of lime in 400 kg mortar is $\dfrac{{10}}{{100}} \times 400kg$ that is equal to $10 \times 4kg = 40kg$ ……(2)
Adding (1) and (2), we will get the sum of quantities of sand and lime in the mortar which will be equal to: (200 + 40) kg = 240 kg.
Therefore, the cement will be equal to the difference of total quantity of mortar and the sum of quantities of cement and lime in it.
So, Quantity of cement in mortar = (400 – 240) kg = 160 kg.
Hence, the required value is 160 kg.
A Percent can also be expressed as a Decimal or a Fraction.
Like here when we said 50% or 40%, we actually meant $\dfrac{{50}}{{100}}$ or $\dfrac{{40}}{{100}}$ of the total thing that was mortar in this question.
"Percent" comes from the latin Per Centum. The latin word Centum means 100, for example a Century is 100 years.