Problems On Numbers - Aptitude MCQ Questions and Solutions with Explanations

81

If the numerator of a fraction is increased by $$\frac{1}{4}$$ and the denominator is decreased byy $$\frac{1}{3}$$, the new fraction obtained is $$\frac{33}{64}$$. What was the original fraction ?

A) $$\frac{3}{7}$$ B) $$\frac{5}{7}$$ C) $$\frac{7}{9}$$ D) Cannot be determined E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the fraction be $$\frac{x}{y}$$
Then,
$$\eqalign{ & \Leftrightarrow \frac{{x + \frac{1}{4}}}{{y - \frac{1}{3}}} = \frac{{33}}{{64}} \cr & \Leftrightarrow \frac{{3\left( {4x + 1} \right)}}{{4\left( {3y - 1} \right)}} = \frac{{33}}{{64}} \cr & \Leftrightarrow \frac{{4x + 1}}{{3y - 1}} = \frac{{33}}{{64}} \times \frac{4}{3} \cr & \Leftrightarrow \frac{{4x + 1}}{{3y - 1}} = \frac{{11}}{{16}} \cr & \Leftrightarrow 16\left( {4x + 1} \right) = 11\left( {3y - 1} \right) \cr & \Leftrightarrow 64x + 16 = 33y - 11 \cr & \Leftrightarrow 64x - 33y = - 27 \cr} $$
Which cannot be solved to find $$\frac{x}{y}$$
Hence, the original fraction cannot be determined from the given data.

82

If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is :

A) 2 B) 3 C) 4 D) 6

Discuss

Answer & Solution

Answer: Option C

Solution:

Let the number be x
Then,
⇔ 2x + 20 = 8x - 4
⇔ 6x = 24
⇔ x = 4

83

Out of six consecutive natural numbers if the sum of first three is 27, what is the sum of the other three ?

A) 24 B) 25 C) 35 D) 36

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the six numbers be, x , (x + 1), (x + 2), (x + 3), (x + 4) and (x + 5)
Then,
⇔ x + (x + 1) + (x + 2) = 27
⇔ 3x + 3 = 27
Required sum :
= (x + 3) + (x + 4) + (x + 5)
= 3x + 12
= (3x + 3) + 9
= 27 + 9
= 36

84

The difference between a two-digit number and the number obtained by interchanging the two digits is 63. Which is the smaller of the two numbers ?

A) 29 B) 70 C) 92 D) Cannot be determined E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the ten's digit be x and unit's digit be y
Then,
$$\eqalign{ & \Leftrightarrow \left( {10x + y} \right) - \left( {10y + x} \right) = 63 \cr & \Leftrightarrow 9\left( {x - y} \right) = 63 \cr & \Leftrightarrow x - y = 7 \cr} $$

85

If the numerator of a fraction is increased by 200% and the denominator is increased by 300%, the resultant fraction is $$\frac{15}{26}$$. What was the original fraction ?

A) $$\frac{8}{11}$$ B) $$\frac{10}{11}$$ C) $$\frac{9}{13}$$ D) $$\frac{10}{13}$$ E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the fraction be $$\frac{x}{y}$$
Then,
$$\eqalign{ & \Leftrightarrow \frac{{x + 200\% {\text{ of }}x}}{{y + 300\% {\text{ of }}y}} = \frac{{15}}{{26}} \cr & \Leftrightarrow \frac{{3x}}{{4y}} = \frac{{15}}{{26}} \cr & \Leftrightarrow \frac{x}{y} = \frac{{15}}{{26}} \times \frac{4}{3} \cr & \Leftrightarrow \frac{x}{y} = \frac{{10}}{{13}} \cr} $$

86

If 50 is subtracted from two-third of number, the result is equal to sum of 40 and one-fourth of that number. What is the number ?

A) 174 B) 216 C) 246 D) 336

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the number be x
Then,
$$\eqalign{ & \Leftrightarrow \frac{2}{3}x - 50 = \frac{1}{4}x + 40 \cr & \Leftrightarrow \frac{2}{3}x - \frac{1}{4}x = 90 \cr & \Leftrightarrow \frac{{5x}}{{12}} = 90 \cr & \Leftrightarrow x = \left( {\frac{{90 \times 12}}{5}} \right) \cr & \Leftrightarrow x = 216 \cr} $$

87

The sum of two numbers is 25 and their difference is 13. Find their product :

A) 104 B) 114 C) 315 D) 325

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the numbers be x and y
Then,
x + y = 25 and x - y = 13
$$\eqalign{ & \Leftrightarrow 4xy = {\left( {x + y} \right)^2} - {\left( {x - y} \right)^2} \cr & \Leftrightarrow 4xy = {\left( {25} \right)^2} - {\left( {13} \right)^2} \cr & \Leftrightarrow 4xy = 625 - 169 \cr & \Leftrightarrow 4xy = 456 \cr & \Leftrightarrow xy = 114 \cr} $$

88

The sum of seven consecutive numbers is 175. What is the difference between twice the largest number and thrice the smallest number ?

A) 7 B) 8 C) 10 D) 12 E) None of these

Discuss

Answer & Solution

Answer: Option E

Solution:

Let the seven numbers be x, (x + 1), (x + 2), (x + 3), (x + 4), (x + 5) and (x + 6)
Then,
⇔ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) = 175
⇔ 7x + 21 = 175
⇔ 7x = 154
⇔ x = 22
Required difference :
= 2(x + 6) - 3x
= 12 - x
= 12 - 22
= -10

89

The number obtained by interchanging the two digits of a two-digit number is lesser than the original number by 54. If the sum of the two digit of the number is 12, then what is the original number ?

A) 28 B) 39 C) 82 D) Cannot be determined E) None of these

Discuss

Answer & Solution

Answer: Option E

Solution:

Let ten's digit = x
Then, unit's digit = (12 - x)
$$\therefore \left[ {10x + \left( {12 - x} \right)} \right] - $$ $$\left[ {10\left( {12 - x} \right) + x} \right]$$ $$ = 54$$
$$\eqalign{ & \Leftrightarrow 18x - 108 = 54 \cr & \Leftrightarrow 18x = 162 \cr & \Leftrightarrow x = 9 \cr} $$
So, ten's digit = 9 and unit's digit = 3
Hence, original number = 93

90

A fraction is such that if the double of the numerator and the triple pf the denominator is changed by +10 percent and -30 percent respectively, then we get 11 percent of $$\frac{16}{21}$$. Find the fraction :

A) $$\frac{2}{25}$$ B) $$\frac{3}{25}$$ C) $$\frac{4}{25}$$ D) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

Let the fraction be $$\frac{x}{y}$$
Then,
$$\eqalign{ & \Leftrightarrow \frac{{110\% {\text{ of 2}}x}}{{70\% {\text{ of 3}}y}} = 11\% {\text{ of }}\frac{{16}}{{21}} \cr & \Leftrightarrow \frac{{22x}}{{21y}} = \frac{{11}}{{100}} \times \frac{{16}}{{21}} \cr & \Leftrightarrow \frac{x}{y} = \left( {\frac{{11}}{{100}} \times \frac{{16}}{{21}} \times \frac{{21}}{{22}}} \right) \cr & \Leftrightarrow \frac{x}{y} = \frac{2}{{25}} \cr} $$