Number System test 2-Solved questions with detailed explanations

6)

If the numerator of a fraction is increased by 240% and the denominator of the fraction is decreased by 50%, the resultant fraction is $2 \frac{5}{6}$ What is the original fraction?

[NABARD (PO) , 2009]

A)
$\frac{1}{4}$
B)
$\frac{2}{3}$
C)
$\frac{5}{12}$
D)
$\frac{4}{11}$
E)
None of these

Answer: Option C

Explanation

Let the original fraction be $\frac{x}{y}$

Then, $\Rightarrow \frac{x + x \times \frac{240}{100}}{y - y \times \frac{50}{100}} = \frac{17}{6} \Rightarrow \frac{x + \frac{12 x}{5}}{y - \frac{y}{2}} = \frac{17}{6} \Rightarrow \frac{\frac{17 x}{5}}{\frac{y}{2}} = \frac{17}{6} \Rightarrow \frac{17 x}{5} \times \frac{2}{y} = \frac{17}{6} \Rightarrow \frac{34 x}{5 y} = \frac{17}{6} [b y c r o s s m u l t i p l l i c a t i o n] \Rightarrow 204 x = 85 y \Rightarrow \frac{x}{y} = \frac{85}{204} = \frac{5}{12} \Rightarrow \frac{x}{y} = \frac{5}{12}$

Hence, option C is correct.

Arithmetics

Discussion

7)

If the numerator of a fraction is increased by 200% and the denominator is increased by 350%. The resultant fraction is $\frac{5}{12}$ . what was the original fraction?

[IOB (PO), 2009]

A)
$\frac{5}{9}$
B)
$\frac{5}{8}$
C)
$\frac{7}{12}$
D)
$\frac{11}{12}$
E)
None of these

Answer: Option B

Explanation

Let the original fraction be $\frac{x}{y}$

Then, numerator= $x + x \times \frac{200}{100} = 3 x$

And denominator= $y + y \times \frac{350}{100} o r \frac{450 y}{100}$

So, fraction = $\frac{N u m e r a t o r}{D e n o m i n a t o r} = \frac{3 x \times 100}{450 y} = \frac{2 x}{3 y}$

Now, = $\frac{2 x}{3 y} = \frac{5}{12}, \frac{x}{y} = \frac{15}{24} = \frac{5}{8}$ .

Hence, Option B is correct.

Arithmetics

Discussion

8)

If the numerator of a fraction is increased by 500% and the denominator is increased by 300%. The resultant fraction is $2 \frac{4}{7}$ . What was the original fraction?

[IOB (PO), 2009]

A)
$\frac{4}{7}$
B)
$\frac{12}{7}$
C)
$\frac{15}{4}$
D)
$\frac{6}{5}$
E)
None of these

Answer: Option B

Explanation

Let the original fraction be $\frac{x}{y}$

Then,

$\Rightarrow \frac{x \times 600}{y \times 400} = \frac{18}{7} \Rightarrow \frac{x}{y} = \frac{72}{42} \Rightarrow \frac{x}{y} = \frac{12}{7} .$

Hence, Option B is correct.

Arithmetics

Discussion

9)

If the numerator of a fraction is increased by 200% and the denominator of the fraction is increased by 150%, the resultant fraction is $\frac{7}{12}$ What is the original 10 fraction?

[Maharashtra (PO), 2008]

A)
$\frac{3}{4}$
B)
$\frac{7}{12}$
C)
$\frac{7}{11}$
D)
$\frac{9}{11}$
E)
None of these

Answer: Option B

Explanation

Let the original fraction be $\frac{x}{y}$

Then,

$\Rightarrow \frac{x \times 300}{y \times 250} = \frac{7}{10} \Rightarrow \frac{x}{y} = \frac{7 \times 5}{10 \times 6} = \frac{35}{60} \Rightarrow \frac{x}{y} = \frac{7}{12}$

Hence, Option B is correct.

Arithmetics

Discussion

10)

If the numerator of a fraction is increased by 20% and its denominator by 25%, then the fraction so obtained is $\frac{3}{5}$ . What is the original fraction?

[Syndicate Bank (PO) Exam, 2004]

A)
$\frac{3}{5}$
B)
$\frac{3}{8}$
C)
$\frac{5}{8}$
D)
Cannot be determined
E)
None of these

Answer: Option C

Explanation

Let the original fraction be $\frac{x}{y}$

Then,

$\Rightarrow \frac{x \times 120}{y \times 125} = \frac{3}{5} R e q u i r e d a n s w e r i s \Rightarrow \frac{x}{y} = \frac{3 \times 125}{5 \times 24} \Rightarrow \frac{x}{y} = \frac{5}{8}$

Hence, Option C is correct.

Arithmetics

Discussion

Number System-Test 2

Answer: Option C

Answer: Option B

Answer: Option B

Answer: Option B

Answer: Option C