CAT 2025 Lesson : Percentages - Of Concept & The Denominator

What percent is 2100 grams of $70$ kg?

Solution

To get an equation, we rewrite the above question as a statement, where the units are the same.

As 1 kg = 1000 grams, the statement here is '$2.1$ kg is ____$\%$ of $70$ kg'.

In this statement, is signifies equal to and of signifies multiplication. Writing this as equation,

$2.1 = x\%$ of $70$

⇒ $2.1 = \dfrac{x}{100} \times 70$

⇒ $x = 3$

$\therefore$ $2.1$kg is 3% of $70$kg.

Alternatively

The question simply means if 70 kg were 100%, then what is 2.1 kg in percentage terms.

$x = \dfrac{2.1}{70} \times$ 100% = 3%

Answer: $3\%$

After working for $24$ hours on a project, Elda realised that $25\%$ of the work still remained. How many more hours will she require to complete the work?

Solution

This question can be solved only if we assume that Elda works at a constant rate. CAT and other tests do not test us with riddles. Therefore, you need to make such assumptions, unless explicitly stated otherwise.

Portion of work completed in $24$ hours = $100\% - 25\% = 75\%$

As Elda works at a constant rate, the statement here is, '$24$ hours is $75\%$ of ____ hours'

$24 = \dfrac{75}{100} \times x$

$x = 32$

$\therefore$ Additional hours taken by Elda = $32 - 24 =$ 8 hours

Answer: $8$ hours