Question

Please find the whole quantity if
5% of whole quantity is 600
12% of whole quantity is 1800
40% of whole quantity is 500

Answer 1

★ How to do :-

Here, we are given with some of the quantity in percentage form and we are also given with the value of that percentage. We are asked to find the total quantity or the whole quantity. Here, we are going to use some other concepts which are very usable and also helps us to find the answer. we are going to use some variables are also known as alphabets which are considered as the whole quantity which we are going to find it. The numericals should also be shifted from one hand side to the other by doing this it's sign changes.

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➤ Solution (1) :-

${\tt \leadsto 5 \bf \% \tt \: \: of \: \: 'x' = 600}$

Write the percentage in fractional form and the 'of' as multiplication sign.

${\tt \leadsto \dfrac{5}{100} \times 'x' = 600}$

Shift the number 600 from RHS to LHS, changing it's sign.

${\tt \leadsto 'x' = \dfrac{100 \times 600}{5}}$

Write the numerator and denominator in lowest form by cancellation method.

${\tt \leadsto 'x' = \dfrac{\cancel{100} \times 600}{\cancel{5}} = \dfrac{20 \times 600}{1}}$

Multiply the numbers to get the answer.

${\tt \leadsto 20 \times 600 = \pink{\underline{\boxed{\tt 'x' = 12000}}}}$

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➤ Solution (2) :-

${\tt \leadsto 12 \bf \% \tt \: \: of \: \: 'x' = 1800}$

Write the percentage in fractional form and the 'of' as multiplication sign.

${\tt \leadsto \dfrac{12}{100} \times 'x' = 1800}$

Shift the number 1800 from RHS to LHS, changing it's sign.

${\tt \leadsto 'x' = \dfrac{100 \times 1800}{12}}$

Write the numerator and denominator in lowest form by cancellation method.

${\tt \leadsto 'x' = \dfrac{100 \times \cancel{1800}}{\cancel{12}} = \dfrac{100 \times 150}{1}}$

Multiply the numbers to get the answer.

${\tt \leadsto 100 \times 150 = \pink{\underline{\boxed{\tt 'x' = 15000}}}}$

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➤ Solution (3) :-

${\tt \leadsto 40 \bf \% \tt \: \: of \: \: 'x' = 500}$

Write the percentage in fractional form and the 'of' as multiplication sign.

${\tt \leadsto \dfrac{40}{100} \times 'x' = 500}$

Shift the number 500 from RHS to LHS, changing it's sign.

${\tt \leadsto 'x' = \dfrac{100 \times 500}{40}}$

Write the numerator and denominator in lowest form by cancellation method.

${\tt \leadsto 'x' = \dfrac{\cancel{100} \times 500}{\cancel{40}} = \dfrac{25 \times 500}{10}}$

Again, we can write the numberator and denominator in lowest form by cancellation method.

${\tt \leadsto 'x' = \dfrac{25 \times \cancel{500}}{\cancel{10}} = \dfrac{25 \times 50}{1}}$

Multiply the numbers to get the answer.

${\tt \leadsto 25 \times 50 = \pink{\underline{\boxed{\tt 'x' = 1250}}}}$

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Hence solved !!