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  • Question
  • A man arranges to pay off a debt of ?3600 in 40 annual installments which form an Arithmetic Progression (A.P). When 30 of the installments are paid, he dies leaving one-third of the debt unpaid . Find the value of the first installment.


  • Options
  • A. 55
  • B. 53
  • C. 51
  • D. 49

  • Correct Answer
  • 51 

    Explanation

    Let us assume the first installment is a and difference between two consecutive installments is d.
    According to question,
    Sum of 40 Installments = 3600
    Apply the formula Sum of first n terms in an Arithmetic Progression = Sn = n/2[ 2a + (n?1)d ]
    where a = the first term, d = common difference, n = number of terms.

    n/2[ 2a + (n?1)d ] = 3600
    Put the value of a, n and d from question,
    40/2[ 2a + (40 ?1)d ] = 3600
    20[ 2a + 39d ] = 3600
    [ 2a + 39d ] = 3600/20 = 180
    2a + 39d = 180...........................(1)

    Again according to given question,
    After paying the 30 installments the unpaid amount = 1/3(total unpaid amount) = 3600 x 1/3
    After paying the 30 installments the unpaid amount = 1200
    So After paying the 30 installments the paid amount = 3600 - 1200 = 2400
    Sum of 30 installments = 2400
    30/2[ 2a + (30 ?1)d ] = 2400
    [ 2a + (30 ?1)d ] = 2400 x 2/30
    2a + 29d = 80 x 2 = 160
    2a + 29d = 160..........................(2)
    Subtract the Eq. (2) from Eq. (1), we will get
    2a + 39d - 2a - 29d = 180 - 160
    10d = 20
    d = 2
    Put the value of d in Equation (1), we will get
    2a + 39 x 2 = 180
    2a = 180 - 78
    a = 102/2
    a = 51
    The value of first installment = a = 51


  • More questions

    • 1. 
      A man buys 3 cows and 18 goats in ? 47,200. Instead if he would have bought 8 cows and 3 goats, he had to pay ? 53,000 more. Cost of one cow is:

    • Options
    • A. ? 10,000
    • B. ? 11,000
    • C. ? 12,000
    • D. ? 13,000
    • Discuss
    • 2. Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

    • Options
    • A. 16 years
    • B. 18 years
    • C. 20 years
    • D. Cannot be determined
    • E. None of these
    • Discuss
    • 3. 
      (17.28 ÷? ) / (3.6 x 0.2) = 2

    • Options
    • A. 120
    • B. 1.20
    • C. 12
    • D. 0.12
    • Discuss
    • 4. 
      If a, b and c are non-zero, a + (1/b) = 1 and b + (1/c) = 1, then the value of abc is

    • Options
    • A. -3
    • B. 1
    • C. -1
    • D. 3
    • Discuss
    • 5. 
      A ladder 15 m long reaches a window which is 9 m above the ground on one side of street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. What is the width of the street:

    • Options
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    • B. 12 m
    • C. 30 m
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    • Discuss
    • 6. 
      4, 2, 3.5, 7.5, 26.25, 118.125

    • Options
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    • C. 3.5
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    • 7. 
      If the square of the sum of two numbers is equal to 4 times of their product. then the ratio of these numbers is:

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    • 8. 
      What is the area of a square having perimeter 68 cm?

    • Options
    • A. 361 sq cm
    • B. 284 sq cm
    • C. 269 sq cm
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    • 9. A and B can do a job together in 7 days. A is 1¾ times as efficient as B. The same job can be done by A alone in :

    • Options
    • A.

      9 1 days
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    • B. 11 days
    • C.

      12 1 days
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    • D.

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    • Discuss
    • 10. 
      Area of a square is 1/2 hectare. The diagonal of the square is?

    • Options
    • A. 250 meter
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