1). A number consists of two digits. The sum of the digits is 10. On reversing the digits of the number, the number decreases by 36. What is the product of the two digits?
View Answer Correct Answer: 21 Let the unit's digit of the number be x and ten's digit be y. Therefore, Number = 10y + x According to the question, x + y = 10 ...(i) \( \Large 10x+y = \left(10x+x\right)36 \) ...(ii) = 10x+y10yx=36 = 9x  9y = 36 = x  y = 4 On adding Eqs. (i) and (ii), we get x + y = 10 \( \Large \frac{xy=4}{2x=6} \) Therefore, x = 3 and y = 7 Therefore, Required product of two digits = \( \Large 3 \times 7 \) = 21
 
2). If a number is multiplied by threefourth of itself, the value thus obtained is 10800. What is that number?
View Answer Correct Answer: 120 Let the number be x. According to the question, \( \Large x \times \left(x \times \frac{3}{4}\right)=10800 \) \( \Large \frac{3x^{2}}{4} = 10800 \) \( \Large x = \sqrt{14400} = 120 \)
 
3). The sum of five consecutive numbers is 190. What is the sum of the largest and the smallest numbers?
View Answer Correct Answer: 76 Let the five consecutive numbers are x2,x1,x,x+ 1,x+ 2. Sum of numbers = 190 Therefore, x  2 + x  1 + x + x + 1 + x + 2 = 190 = 5x = 190 Therefore, x = 38 Sum of largest and smallest numbers = 190 = x + 2 + x  2 = 2x = \( \Large 2 \times 38 \) = 76
 
4). The product of two consecutive odd numbers is 19043. Which is the smaller one?
View Answer Correct Answer: 137 Let the two consecutive odd numbers are x and x + 2. According to the question, \( \Large x \left(x+2\right)=19043 \) \( \Large x^{2}+2x19043=0 \) \( \Large x^{2}+139x137x19043=0 \) \( \Large x \left(x+139\right)137 \left(x+139\right)=0 \) \( \Large \left(x+139\right) \left(x137\right)=0 \) = x = 137, 139 x = 137 [ignore ve sign] So, the smallest one is 137.
 
5). If the threefourth of a number is subtracted from the number, the value so obtained is 163. What is that number?
View Answer Correct Answer: 652 Let the number be x.
 
6). The sum of two numbers is 10. Their product is 20. Find the sum of the reciprocals of the two numbers.
View Answer Correct Answer: \( \Large \frac{1}{2} \) Let the numbers be x and y, Then, x + y = 10 ...(i) and xy = 20 ...(ii) Therefore, \( \Large \left(xy\right)^{2}= \left(x+y\right)^{2}4xy \) \( \Large \left(xy\right)^{2}= \left(10\right)^{2}4 \times 20=20 \) \( \Large x  y = \sqrt{20} = 2\sqrt{5} \) ...(iii) On adding Eqs. (i) and (iii), we get x + y = 10 \( \Large x  y = 2\sqrt{5} \) \( \Large 2x = 10 + 2\sqrt{5} \) Therefore, \( \Large x = 5 + \sqrt{5} \) On putting the value of x in Eq. (i), we x + y = 10 => \( \Large 5 + \sqrt{5} + y = 10 \) Therefore, \( \Large y = 5  \sqrt{5} \) Sum of reciprocals of x and y = \( \Large \frac{1}{x} \) + \( \Large \frac{1}{y} \) \( \Large =\frac{1}{5+\sqrt{5}}+\frac{1}{5\sqrt{5}}= \frac{5\sqrt{5}+5+\sqrt{5}}{ \left(5+\sqrt{5}\right) \left(5\sqrt{5}\right) } \) \( \Large = \frac{10}{ \left(5\right)^{2}  \left(\sqrt{5}\right)^{2} } = \frac{10}{20} = \frac{1}{2} \)
 
7). Five times of a positive integer is equal to 3 less than twice the square of that number. Find the number.
View Answer Correct Answer: 3 Let the number be x.
 
8). A man has given onefourth part of his property to his daughter, half part to his sons and onefifth part given as charity. How much part of his property he has given?
View Answer Correct Answer: \( \Large \frac{19}{20} \) Total share given by a person
 
9). A chocolate has 12 equal pieces. Manju gave \( \Large \frac{1}{4} \)th of it to Anju, \( \Large \frac{1}{3} \)rd of it to Sujata and \( \Large \frac{1}{6} \)th of it to Fiza. The number of pieces of chocolate left with Manju is
View Answer Correct Answer: 3 The number of pieces of chocolate with Maniu = \( \Large 1  \left(\frac{1}{4}+\frac{1}{3}+\frac{1}{6}\right) \) = \( \Large 1  \left(\frac{3 + 4 + 2}{12}\right) \) = \( \Large 1  \frac{9}{12} = \frac{12  9}{12} = \frac{3}{12} \) Hence, number of pieces of chocolate left with Manju is 3.
 
10). A number consists of two digits whose sum is 10. If the digits of the number are reversed, then the number decreased by 36. Which of the following is/are correct? I. The number is divisible by a composite number. II. The number is a multiple of a prime number.
View Answer Correct Answer: Only II Let the twodigit number be 10x + y.

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