Name: Opposite & Inverse of a Rational Number
Uploaded: 2019-07-19
Duration: 3 min 23 s
Description: Taking what we have learnt about number lines, you know that every number has an opposite. But what about rational numbers? Do they have opposites too? Yes!...

Question

Ram donated $\frac{1}{10}$ of his salary to an orphanage, $\frac{1}{3}$ of his salary spent on food, $\frac{1}{4}$ of salary on rent and electricity and $\frac{1}{20}$ of his salary on telephone. This month he donated $₹ 5000$ in Prime Minister relief fund for Uttarakhand victims. He was left with $₹ 3000$ with him, find his monthly salary. Should we donate the money for needy people? What values are being promoted $?$

Accepted Answer

Let Ram's salary $= x$

Then donation to orphanage $\frac{1}{4}$

Amount spent on food $₹ 3000$

Spend on rent and electricity $= x \times \frac{1}{4} = \frac{x}{4}$

Spent on telephone $= x \times \frac{1}{20} = \frac{x}{20}$

Amount left $= x - (\frac{x}{10} + \frac{x}{3} + \frac{x}{4} + \frac{x}{20})$

$= x - (\frac{6 x + 20 x + 15 x + 3 x}{60}) = x - (\frac{44 x}{60}) = x - \frac{44 x}{60} = \frac{60 x - 44 x}{60} = \frac{16 x}{60}$

Amount given to Prime Minister relief fund $= ₹ 5000$

And amount left $= ₹ 3000$

$∴ \frac{16}{60} x = 5000 + 3000 \frac{16}{60} x = 8000 16 x = 8000 \times 60 x = \frac{8000 \times 60}{16} = 500 \times 60 = 30000$

$x = \frac{8000 \times 60}{16} = 30, 000$
So, Ram's monthly salary is $₹ 30000$

Donation to a needy institution is good, Also donation to PM relief fund is an act of kindness.

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