# Gaurav’s income is 160000 per year. He pays 15% of this as house rent and 10% of the remainder on his child’s education. The money left with him is

$

A.\;{\text{ 136000}} \\

B.\;{\text{ 120000}} \\

C.\;{\text{ 122400}} \\

D.\;{\text{ 14000}} \\

$

Answer

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362.4k+ views

Hint: In this question Gaurav’s income is 160000 per year and he has to pay some of his expenses like house rent and child’s education. So the overall sum of the amount left with him will eventually be that portion of his salary that is left after paying all expenses, so use this concept to reach the answer.

Complete step-by-step answer:

Let the money left with him be x Rs after paying house rent and child education.

Given data

Gaurav’s income $ = 160000$ Rs.

He pays 15% of this as house rent.

Let the money left with him after paying house rent be y Rs.

So, the remainder of the Gaurav income (y) is Gaurav income minus 15% of Gaurav income.

$ \Rightarrow y = 160000 - \dfrac{{15}}{{100}} \times 160000$

$ \Rightarrow y = 160000 - 15 \times 1600$

$ \Rightarrow y = 160000 - 24000 = 136000$ Rs.

Now he pays 10% of the remainder on his child education.

So, the money left (x) with him after paying house rent and child education is y minus 10% of y

$ \Rightarrow x = y - \dfrac{{10}}{{100}}\left( y \right)$

$ \Rightarrow x = 136000 - \dfrac{{10}}{{100}}\left( {136000} \right)$

$ \Rightarrow x = 136000 - \left( {13600} \right)$

$ \Rightarrow x = 122400$ Rs.

So, the money left with him after paying house rent and child education is 122400 Rs.

Hence, option (c) is correct.

Note: Whenever we face such type of problems the key concept is to deduct the expenses from his income step by step, as these expenses which he will be playing plays a significant role in the amount that will be left with him. This calculation of expenses in order to deduct them from income will help you get on the right track to reach the answer.

Complete step-by-step answer:

Let the money left with him be x Rs after paying house rent and child education.

Given data

Gaurav’s income $ = 160000$ Rs.

He pays 15% of this as house rent.

Let the money left with him after paying house rent be y Rs.

So, the remainder of the Gaurav income (y) is Gaurav income minus 15% of Gaurav income.

$ \Rightarrow y = 160000 - \dfrac{{15}}{{100}} \times 160000$

$ \Rightarrow y = 160000 - 15 \times 1600$

$ \Rightarrow y = 160000 - 24000 = 136000$ Rs.

Now he pays 10% of the remainder on his child education.

So, the money left (x) with him after paying house rent and child education is y minus 10% of y

$ \Rightarrow x = y - \dfrac{{10}}{{100}}\left( y \right)$

$ \Rightarrow x = 136000 - \dfrac{{10}}{{100}}\left( {136000} \right)$

$ \Rightarrow x = 136000 - \left( {13600} \right)$

$ \Rightarrow x = 122400$ Rs.

So, the money left with him after paying house rent and child education is 122400 Rs.

Hence, option (c) is correct.

Note: Whenever we face such type of problems the key concept is to deduct the expenses from his income step by step, as these expenses which he will be playing plays a significant role in the amount that will be left with him. This calculation of expenses in order to deduct them from income will help you get on the right track to reach the answer.

Last updated date: 24th Sep 2023

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