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  • Question
  • The difference between the squares of two numbers is 256000 and the sum of the numbers is 1000. The numbers are


  • Options
  • A. 600, 400
  • B. 628, 372
  • C. 640, 360
  • D. None of these

  • Correct Answer
  • 628, 372 

    Explanation

    Let us assume the numbers are a and b.
    According to question,
    a2 - b2 = 256000 .......................(1)
    and a + b = 1000 .........................(2)
    On dividing the Equation (1) with Equation (2),
    (a2 - b2)/(a + b) = 256000/1000
    (a2 - b2)/(a + b) = 256
    (a + b)(a - b)/(a + b) = 256
    a - b = 256...............................(3)
    Add the equation (2) and (3), we will get
    a + b + a - b = 1000 + 256
    2a = 1256
    a = 628
    Put the value of a in equation (2), we will get
    658 + b = 1000
    b = 1000 - 628
    b = 372
    So answer is 628 , 372.


  • Linear Equation problems


    Search Results


    • 1. 
      The sum of two numbers is 25 and their difference is 13. Find their product.

    • Options
    • A. 104
    • B. 114
    • C. 315
    • D. 325
    • Discuss
    • 2. 
      Ram and Mohan are friends. Each has some money. If Ram gives ? 30 to Mohan, Then Mohan will have twice the money left with Ram. But if Mohan gives ? 10 to Ram, Then Ram will have thrice as much as is left with Mohan. How much money does each have?

    • Options
    • A. ?62,?34
    • B. ?6,?2
    • C. ?170,?124
    • D. ?43,?26
    • Discuss
    • 3. 
      In the certain party, there was a bowl of rice for every two guests , a bowl of juice for every three of them and a bowl of meat for every four of them. If there were all 65 bowls of food , then how many guests were there in the party?

    • Options
    • A. 65
    • B. 24
    • C. 60
    • D. 48
    • Discuss
    • 4. 
      A driver's income consists of his salary and tips. during one week his tips were 5/4 of his salary. what fraction of his income came from tips?

    • Options
    • A. 4/9
    • B. 5/9
    • C. 5/8
    • D. 5/4
    • Discuss
    • 5. 
      If the sum of one-half and one-fifth of the number exceeds one-third of that number by 7 1/3 , the number is

    • Options
    • A. 15
    • B. 18
    • C. 20
    • D. 30
    • Discuss
    • 6. 
      Two-fifths of one -fourth of three -seventh of a number is 15. What is half of that number?

    • Options
    • A. 96
    • B. 196
    • C. 94
    • D. None of these
    • Discuss
    • 7. 
      The numbers are such that the square of one is 224 less than 8 times the square of the other. If the numbers be in the ratio 3 : 4, the numbers are

    • Options
    • A. 3 , 6
    • B. 4 , 8
    • C. 6 , 8
    • D. 6 , 4
    • Discuss
    • 8. 
      A person on tour has total ?360 for his daily expenses. He decides to extend his tour programme by 4 days which leads to cutting down daily expenses by ?3 a day . The numbers of days of tour are :

    • Options
    • A. 15
    • B. 20
    • C. 18
    • D. 16
    • Discuss
    • 9. 
      The sum of three consecutive odd numbers is 20 more than the first of these numbers.What is the middle number?

    • Options
    • A. 7
    • B. 9
    • C. 11
    • D. Data inadequate
    • Discuss
    • 10. 
      The auto-rickshaw fare consists of a fixed charge together with the charge for the distance covered. For a journey of 10 km, the charge paid is ?85 and for a journey of 15 km, the charge paid is ?120. The fare for a journey of 25 km will be

    • Options
    • A. ?175
    • B. ?190
    • C. ?180
    • D. ?225
    • Discuss


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