Problems on Numbers

Problems on Numbers

Decimal Fraction :- Fractions in which denominators are powers of 10.

• Multiplication of decimal fractions- after multiplication of given numbers, decimal point is marked off to obtain as many places of decimal as is the sum of number of decimal places in the given number. 

   Example: 0.2 × 0.02 × 0.002 = 0.000008 

• Division of decimal fractions : after division of given numbers, put decimal point as many places of decimal as there are in dividend. 

   Example : 0.0204 ÷ 17 = 0.0012

• Recurring Decimal - If in a decimal fraction,  a figure or a set of figures is repeated continuously. 

Example- 1/3 = 0.3333....

• Pure Recurring Decimal - A decimal fraction in which all the figures after decimal point are repeated.
• Mixed Recurring Decimal - A decimal fraction in which some figures do not repeat and some of them are repeated. 

         Example - 0.173333.....

Do it Yourself 

1.          1. 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
2.    What is the sum of two consecutive even numbers, the difference of whose squares is 84?
         A. 34               B. 38               C. 42               D. 46
3. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is:
        A. 18               B. 24               C. 42               D. 81
4.    If the numerator of a fraction is increased by 2 and the denominator is increased by 3, the fraction becomes 7/9 and if both the numerator as well as the denominator are decreased by 1, the fraction becomes 4/5. What is the original fraction?
                A. 5/6             B. 9/11           C. 13/16         D. 17/21
 
5.    In a pair of fractions, fraction A is twice the fraction B and the product two fractions is 2/25. What is the value of fraction A?
                A. 1/5             B. 1/25           C. 2/5              D. Data inadequate
 
6.    A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by :
           A. 3                 B. 5                 C. 9                 D. 11
 
7.    The sum of two numbers is 40 and their product is 375. What will be the sum of their reciprocals?
    A. 1/40          B. 8/75           C.75/4                        D.75/8
 
8.    Of two numbers, 4 times the smaller one is less than 3 times the larger one by 5. If the sum of the numbers is larger than 6 times their differences by 6, find the two numbers. (Ans.59 & 43)
 
9.    Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the no.
                A. 3                 B. 10               C. 17               D. 20
10. How many digits will be there to the right of the decimal point in the product of 95.75 and 0.02554?
                A. 5                 B. 6                 C. 7                 D. None
 
11. If 50 is subtracted from two-third of a no., the result is equal to sum of 40 and one-fourth of that no. What is the no.?
               A.    174           B. 216             C. 246             D. 336
 
12. If 81% of a no. is added to 380, then the result is the no. itself. Find the no.?
                A. 2400          B. 1800          C. 2200          D. 2000
 
13. The ratio of two numbers is 8 : 9 & their sum is 935. Find the greater of the two numbers.
                A. 495                        B.505              C. 515             D. 525
 
14. Find the fraction of 0.5055555…..
                A. 455/900    B. 453/900     C. 457/900     D. 555/900
 
15. If 13930/1.75 = 7960, what is the value of 27860/17.5 = ?
                A. 1692                      B. 1792                      C. 1592          D. 1892
 
16. Find the fraction of 0.426262626.
                A. 442/990    B.452/990                  C. 422/990     D. 432/990
 
17. 652/900 – 552/900 + 452/900 = ?
                A. 0.5133333            B.0.7133333 C. 0.4133333      D. 0.6133333
 
18. 85/8 divided by 2 is
                A. 5.3125       B.5.5125                    C. 5.4125                   D. 5.2125
 
19. A fraction is greater than twice its reciprocal by 71/91. What is the frcation?
                A. 15/9                       B.17/11                      C. 13/7                       D. 14/9
 
20. The sum of the squares of three numbers is 532 and the ratio of the first to the second as also of the second to the third is 3 : 2. What is the second
number?
                A.    12              B. 18               C. 15               D.21
21. When 48 is subtracted from a number it reduces to its 70%. What is one-fourth of that number ?
                A. 20               B. 40               C. 60               D. 80
22. When a number is divided by 4, the quotient is 28, what is the number?
                 A. 112                        B. 46               C. 86               D. 96
23. Evaluate [(18 − 6) ÷ 4] + [72 – 12 ÷ 3 of 2]
                    A. 76               B. 72               C. 75               D. 73
24. If 45 – [28 – {37 – (15 − *)}] = 58, then * is equal to :
                   A. −29                        B. −19                        C. 19               D. 29
25. By how much is three-fifth of 350 greater than four-seventh of 210?
                   A. 95               B. 110             C. 120             D. None

      26. The sum of two numbers is equal to 30 and their difference is 6. What is the ratio of the two numbers?
                    A. 8 : 7         B. 5 : 1            C. 3 : 2                 D. 2 : 1

        27. A student,  instead of multiplying,  divided a given number by 9/23, by mistake.  If his answer was 896 more than the correct answer,  then what is the given number? (Ans.414)

         28. There are two sections A and B, of a class.  If 15 pupils will be sent from Section A to Section B, then the number in both the sections will be equal. If 20 pupils will be sent from Section B to Section A, the number double of that of Section B. What is the actual strength of Section A? 
                               A. 80                   B.90                 C.100                     D. 120
29. The sum of a two digit number and  40% of the number obtaining by reversing its is 87.4. If sum of digits of original number is 11, then 60% of the original number :-  (Ans. 39)

      

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