Basic Maths: Test 53

This is an assessment test.
These tests focus on the basics of Maths and are meant to indicate your preparation level for the subject.
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Basic Maths: Test 53

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Question 1

Rahul's monthly salary is one and a half times Harsh's monthly salary, Nikhil's monthly salary is five-fourth of Rahul's monthly salary. If the total of the monthly salaries of all the three is Rs.1.83,750. what is Nikhil's monthly salary?

A	Rs.42,000
B	Rs.68,500
C	Rs.78,750
D	Rs.63,000

Question 1 Explanation:

$\begin{align} & Let\,\,\,Harsh's\,\,\,monthly\,\,\,income\,\,be\,\,Rs.\,x. \\ & Rahul's\,\,\,monthly\,\,\,income\,\,=Rs.\,\frac{3x}{2} \\ & Nikhil's\,\,monthly\,\,\,income\,\,=Rs.\,\frac{15x}{8} \\ & Therefore\,\,x+\frac{3x}{2}+\frac{15x}{8}=183750 \\ & \Rightarrow \frac{8x+12x+15x}{8}=183750 \\ & \Rightarrow 35x=183750\times 8 \\ & \Rightarrow x=\frac{183750\times 8}{35}=42000 \\ & Therefore\,\,Nikhil's\,\,\,monthly\,\,\,\,income\, \\ & =Rs.\,\left( \frac{15}{8}\times 42000 \right) \\ & =Rs.78750 \\ \end{align}$

Question 2

$\left( 41\times 71+123\times 23+82\times 25 \right)$ is equal to

A	779000
B	7090
C	7790
D	70900

Question 2 Explanation:

$\begin{align} & =\left( 41\times 71+123\times 23+82\times 25 \right) \\ & =41\,\left( 71+3\times 23+2\times 25 \right) \\ & =41\,\left( 71+69+50 \right) \\ & =41\times 190=7790 \\ \end{align}$

Question 3

$\left( \frac{3.77\times 3.77\times 3.77-1.77\times 1.77\times 1.77}{3.77\times 3.77+3.77\times 1.77+1.77\times 1.77} \right)$ is equal to

A	−2
B	0.2
C	−0.2
D	2

Question 3 Explanation:

Let 3.77 = a
And 1.77= b
Therefore expression
$\begin{align} & =\frac{{{a}^{3}}-{{b}^{3}}}{{{a}^{2}}+ab+{{b}^{2}}} \\ & =a-b=3.77-1.77=2.0 \\ \end{align}$

Question 4

$5\frac{2}{71}\times 9\frac{12}{17}\times 12\frac{10}{11}+4\frac{3}{4}=?$