Number System-Test 3

Answer: Option D

Explanation

let the number be 'x'

Given that the difference between the number is $\frac{3}{5}$ of the number is 40

 $$\begin{gathered} = x-\frac{3}{5x}=40 \\ = \frac{5x+(-3x)}{5}=40 \\ = \frac{2x}{5}=40 [multiply both sides of the equation by \frac{5}{2}] \\ = \frac{5}{2}\times \frac{2x}{5}=\frac{5}{2}\times 40 \\ = \frac{1}{2}\times 2x=\frac{5}{2}\times 40 \\ = x=\frac{5}{2}\times 40 \\ =x=100 \end{gathered}$$

Hence, Option D is correct.

Answer: Option D

Explanation

let the number 'x'

According to the question

$$\begin{gathered} = \frac{1}{4}x+5=\frac{1}{3}x-5 \\ = \frac{x}{4}+5=\frac{x-3\times 5}{3} \\ =\frac{x}{4}+5=\frac{x-15}{3} [multiply both sides by 12] \\ = 12\times \frac{x}{4}+12\times 5=12\times \frac{x-15}{3} \\ =3x+60=4(x-15) \\ =3x+60=4x-60 \\ =x=120 \end{gathered}$$

Hence, Option D is correct.

Answer: Option C

Explanation

Let the number is 'x'

According to the question

The number is tripled= 3x

Then, added 3= (3x+3)

Resultant is doubled = 2(3x+3)

Given, 30

⇒ 2(3x+3)=30

⇒ 6x+6=30

⇒ 6x=24

⇒ x=4

∴ The number is '4'

Hence, Option C is correct.

Answer: Option C

Explanation

According to the question

Sum of two numbers = x+y=18  ---Eq(1)

Four times of one = 4x

and five times the other number = 5y

Now, 4x-5y=0  ---Eq(2)

From Eq(1) we get,

⇒  x+y=18

⇒ x=18-y

Substitute 'x' in Eq(2) we get,

⇒ 4(18-y)-5y=0

⇒ 72-4y=5y

 ⇒ -4y-5y=-72

 ⇒ -9y=-72   [divide both sides by '-9']

we get,

 ⇒ y=8

Substitute 'y' value in Eq(2) we get,

 ⇒ 4x=5×(8)

 ⇒ 4x=40

 ⇒ x=10

∴ x=10, y=8

The bigger of the two number is x=10

Hence, option C is correct.

Answer: Option C

Explanation

According to te question

Let the first even number be 'x'

And the consecutive even numbers be x,x+2,x+4,x+6

Sum of four consecutive numbers = 284

⇒ x+(x+2)+(x+4)+(x+6)=284

⇒ 4x+12=284

⇒ 4x=284-12

⇒ 4x=272   [divide both sides by '4']

We get,

⇒ x=68

So, '68' is the smallest number followed by 70,72,74.

Hence, Option C is correct.