Practice MCQ Questions and Answer on Problems on Numbers

61.

If the difference between the reciprocal of a positive proper fraction and the fraction itself be $$\frac{9}{20}$$, then the fraction is :

• (A) $$\frac{3}{5}$$
• (B) $$\frac{4}{5}$$
• (C) $$\frac{5}{4}$$
• (D) $$\frac{3}{10}$$

Show Answer

 Let the fraction be $$\frac{a}{1}$$ Then, $$\eqalign{ & \Leftrightarrow \frac{1}{a} - a = \frac{9}{{20}} \cr & \Leftrightarrow \frac{{1 - {a^2}}}{a} = \frac{9}{{20}} \cr & \Leftrightarrow 20 - 20{a^2} = 9a \cr & \Leftrightarrow 20{a^2} + 9a - 20 = 0 \cr & \Leftrightarrow 20{a^2} + 25a - 16a - 20 = 0 \cr & \Leftrightarrow 5a\left( {4a + 5} \right) - 4\left( {4a + 5} \right) = 0 \cr & \Leftrightarrow \left( {4a + 5} \right)\left( {5a - 4} \right) = 0 \cr & \Leftrightarrow a = \frac{4}{5}\,\,\,\,\,\,\,\,\left[ {\because a \ne - \frac{5}{4}} \right] \cr} $$

62.

243 has been divided into three parts such that half of the first part, one-third of the second part and one-fourth of the third part are equal. The largest part is :

• (A) 74
• (B) 86
• (C) 92
• (D) 108

Show Answer

 Let the three parts be A, B and C $$\eqalign{ & {\text{Let }}\frac{A}{2} = \frac{B}{3} = \frac{C}{4} = x \cr & {\text{Then, }}A = 2x,B = 3x{\text{ and }}C = 4x \cr & {\text{So, }}A:B:C = 2:3:4 \cr & \therefore {\text{Largest part :}} \cr & = \left( {243 \times \frac{4}{9}} \right) \cr & = 108 \cr} $$

63.

The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

• (A) 20
• (B) 23
• (C) 169
• (D) None of these

Show Answer

 Let the numbers be x and y Then, xy = 120 and x2 + y2 = 289 ∴ (x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529 ∴ x + y = $$\sqrt {529} $$  = 23

64.

What is the sum of two consecutive even numbers, the difference of whose squares is 84 ?

• (A) 34
• (B) 38
• (C) 42
• (D) 46

Show Answer

 Let the numbers be x and x + 2 Then, (x + 2)2 - x2 = 84 ⇔ 4x + 4 = 84 ⇔ 4x = 80 ⇔ x = 20 ∴ Required sum = x + (x + 2) = 2x + 2 = 42

65.

Three-forth of a number is 60 more than its one-third. The number is :

• (A) 84
• (B) 108
• (C) 144
• (D) None of these

Show Answer

 Let the number be x Then, $$\eqalign{ & \Leftrightarrow \frac{3}{4}x - \frac{1}{3}x = 60 \cr & \Leftrightarrow \frac{{5x}}{{12}} = 60 \cr & \Leftrightarrow x = \left( {\frac{{60 \times 12}}{5}} \right) \cr & \Leftrightarrow x = 144 \cr} $$

66.

The ratio between a two-digit number and the sum of the digits of that number is 4 : 1. If the digit in the unit's place is 3 more than the digit in the ten's place, then the number is ?

• (A) 24
• (B) 36
• (C) 63
• (D) 96

Show Answer

 Let the ten's digit be x Then, units digit = x + 3 Number = 10x + (x + 3)               = 11x + 3 Sum of digits = x + (x + 3)                       = 2x + 3 $$\eqalign{ & \therefore \frac{{11x + 3}}{{2x + 3}} = \frac{4}{1} \cr & \Leftrightarrow 11x + 3 = 8x + 12 \cr & \Leftrightarrow 3x = 9 \cr & \Leftrightarrow x = 3 \cr} $$ Hence, Required number = 11x + 3 = 11 × 3 + 3 = 36

67.

If the product of two numbers is 5 and one of the number is $$\frac{3}{2}$$, then sum of two numbers is :

• (A) $$4\frac{1}{3}$$
• (B) $$4\frac{2}{3}$$
• (C) $$4\frac{5}{6}$$
• (D) $$5\frac{1}{6}$$

Show Answer

 Let two numbers be a and b Given ab = 5 and a = $$\frac{3}{2}$$ $$\eqalign{ & \Rightarrow b = \frac{5}{a} \cr & \Rightarrow b = \frac{5}{{\frac{3}{2}}} \cr & \Rightarrow b = \frac{{5 \times 2}}{3} \cr & \Rightarrow b = \frac{{10}}{3} \cr} $$ Required sum of : ⇒ a + b = $$\frac{{3}}{2}$$ + $$\frac{{10}}{3}$$ L.C.M. of 2 and 3 = 6 ⇒ a + b = $$\frac{{9 + 20}}{6}$$ ⇒ a + b = $$\frac{{29}}{6}$$ ⇒ a + b = $$4\frac{{5}}{6}$$

68.

If one-third of one-fourth of a number is 15, then three-tenth of that number is:

• (A) 35
• (B) 36
• (C) 45
• (D) 54

Show Answer

 $$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{number}}\,{\text{be}}\,x \cr & {\text{Then}},\,\frac{1}{3}\,{\text{of}}\,\frac{1}{{4\,}}\,{\text{of}}\,x = 15\cr & \Rightarrow \, x = 15 \times 12 = 180 \cr & {\text{So,}}\,{\text{required}}\,{\text{number}} \cr & = {\frac{3}{{10}} \times 180} \cr & = 54 \cr} $$

69.

If a number is added to two-fifths of itself, the value so obtained is 455. What is the number ?

• (A) 325
• (B) 350
• (C) 400
• (D) 420

Show Answer

 Let the number be x Then, $$\eqalign{ & \Leftrightarrow x + \frac{2}{5}x = 455 \cr & \Leftrightarrow \frac{7}{5}x = 455 \cr & \Leftrightarrow x = \left( {\frac{{455 \times 5}}{7}} \right) \cr & \Leftrightarrow x = 325 \cr} $$

70.

A number is double and 9 is added. If the resultant is trebled, it becomes 75. What is that number ?

• (A) 3.5
• (B) 6
• (C) 8
• (D) None of these

Show Answer

 Let the number be x Then, ⇔ 3(2x + 9) = 75 ⇔ 2x + 9 = 25 ⇔ 2x = 16 ⇔ x = 8