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Home Aptitude Linear Equation See What Others Are Saying!
  • Question
  • A number 15 is divided into 3 parts which are in Arithmetic Progression (A.P) and the sum of their squares is 83. What will be the smallest number?


  • Options
  • A. 5
  • B. 3
  • C. 6
  • D. 8

  • Correct Answer


  • Explanation

    Let us assume the second number is a and the difference between consecutive numbers is d.
    According to Arithmetic progression,
    First number = a - d
    Second number = a
    Third number = a + d
    According to question,
    Sum of the all three numbers = 15
    a - d + a + a + d = 15
    3a = 15
    a = 5
    Again according to given question,
    sum of square of the 3 numbers = 83
    (a - d) 2 + a 2 + (a + d) 2 = 83
    apply the algebra formula
    a 2 + d 2 - 2ad + a 2 + a 2 + d 2 + 2ad = 83
    3a 2 + 2d 2 = 83
    Put the value of a in above equation.
    3 x 5 2 + 2d2 = 83
    3 x 25 + 2d2 = 83
    75 + 2d2 = 83
    2d 2 = 83 - 75
    2d 2 = 8
    d 2 = 8/2
    d 2 = 4
    d = 2
    Put the value of a and d in below equation.
    First number = a - d = 5 - 2 = 3
    Second number = a = 5
    Third number = a + d = 5 + 2 = 7
    The smallest number is 3.


  • More questions

    • 1. Find the odd word/letters/number from the given alternatives.

    • Options
    • A. Tabla
    • B. Tanpura
    • C. Sarod
    • D. Sitar
    • Discuss
    • 2. 20% discount is offered on an item. By applying a promo code the customer wins 5% cash back. What is the effective discount?

    • Options
    • A. 24 percent
    • B. 25.2 percent
    • C. 25 percent
    • D. 6 percent
    • Discuss
    • 3. A shopkeeper, sold almonds at the rate Rs 1250 per kg and bears a loss of 7%. Now if he decides to sell it at Rs 1375 per kg, what will be the result?

    • Options
    • A. 4.6 percent gain
    • B. 2.3 percent loss
    • C. 2.3 percent gain
    • D. 4.6 percent loss
    • Discuss
    • 4. If x+1/x = 2, then the value of x7+2/x6 is equal to?

    • Options
    • A. 0
    • B. 1
    • C. 2
    • D. 3
    • Discuss
    • 5. A man is running at the speed of 20 km/hr. What is time (in seconds) taken by man to cover one round of a circular garden of radius 350 metres?

    • Options
    • A. 412
    • B. 336
    • C. 396
    • D. 376
    • Discuss
    • 6. The rate of working of A and B are in the ratio of 2:3. The number of days taken by them to finish the work is in the ratio:

    • Options
    • A. 2:3
    • B. 4:9
    • C. 3:2
    • D. 9:4
    • Discuss
    • 7. Find the odd word/letters/number from the given alternatives.

    • Options
    • A. CBED
    • B. JILK
    • C. TSVU
    • D. VZXY
    • Discuss
    • 8. In a shop 4.5% of 1500 kg toor dal was sold. Find the quantity sold

    • Options
    • A. 64.5 kg.
    • B. 63.5 kg.
    • C. 70 kg
    • D. 67.5 kg
    • Discuss
    • 9. The average age of Vishal and Raghavendra is 24 years. If a new person Veerender is also included, the average age is increased by 1.5 years. What is the age of Veerender?

    • Options
    • A. 28.5 yrs
    • B. 29.5 yrs
    • C. 30.5 yrs
    • D. 27 yrs
    • Discuss
    • 10. If a merchant offers a discount of 4% on the list price, then she makes a loss of 10%. What % profit or % loss will she make if she sells at a discount of 20% of the list price?

    • Options
    • A. 25 percent loss
    • B. 4 percent loss
    • C. 50 percent profit
    • D. 26 percent profit
    • Discuss


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