Problems On Numbers

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31 The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is :

A
$$\frac{1}{289}$$
B
$$\frac{289}{290}$$
C
$$\frac{290}{289}$$
D
$$289$$

32 If a number is multiplied by three-fourth of it'self, the value thus obtained is 10800. What is that number?

A
210
B
180
C
120
D
160

33 If the numerator of a certain fraction is increased by 2 and the denominator is increased by 1, then the resulting fraction is equal to $$\frac{1}{2}$$. If however, the numerator is increased by 1 and denominator is decreased by 2, then the resulting fraction 3/5. Find the faction:

A
2/9
B
$$\frac{2}{7}$$
C
$$\frac{3}{7}$$
D
3/11

34 One-fourth of a number exceeds it's one-seventh by 24. What is the number?

A
124
B
224
C
324
D
424

35 The difference between the numerator and the denominator of a fraction is 5. If 5 is added to it's denominator, the fraction is decreased by $$1\frac{1}{4}$$. Find the value of the fraction:

A
$$\frac{1}{6}$$
B
$$2\frac{1}{4}$$
C
$$3\frac{1}{4}$$
D
$$6$$

36 In an examination paper of five questions, 5% of the candidates answered all of them and 5% answered none. Of the rest, 25% candidates answered only one question and 20% answered 4 questions. If 396 candidates answered either 2 questions or 3 questions, the number of candidates that appeared for the examination was

A
800
B
1000
C
850
D
900

37 If 1 is added to the denominator of a traction, the fraction becomes $$\frac{1}{2}$$. If 1 is added to the numerator of the fraction, the fraction becomes 1. The fraction is :

A
1/3
B
$$\frac{2}{3}$$
C
4/3
D
5/3

38 The difference between a two-digit number and the number obtained by interchanging the two digit's of the number is 18. The sum of the two digit's of the number is 12. What is the product of the digit's of two-digit number?

A
35
B
27
C
32
D
40

39 The difference between two numbers is 18. If four times the second number is less than three times the first number by 18, then what is the sum of these two numbers?

A
100
B
80
C
86
D
92

40 Out of three given numbers, the first number is twice the second and thrice the third. If the average of these three numbers is 154, then what is the difference between the first and the third numbers?

A
126
B
42
C
168
D
52