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  • Question

  • 1/(1 x 4) + 1/(4 x 7) + 1/(7 x 10) + 1/(10 x 13) + 1/(13 x 16) =?


  • Options
  • A. 5/16
  • B. 3/16
  • C. 7/16
  • D. 11/16

  • Correct Answer
  • 5/16 

    Explanation

    Given expression can be written as
    = 1/(1 x 4) + 1/(4 x 7) + 1/(7 x 10) + 1/(10 x 13) + 1/(13 x 16)
    = 1/3{ 3/(1 x 4) + 3/(4 x 7) + 3/(7 x 10) + 3/(10 x 13) + 3/(13 x 16) }
    = 1/3{ (4 - 1)/(1 x 4) + (7 - 4)/(4 x 7) + (10 - 7 )/(7 x 10) + (13 - 10)/(10 x 13) + (16 - 13/(13 x 16) }
    = 1/3[(1 - 1/4) + (1/4 - 1/7) + (1/7 - 1/10) + (1/10 - 1/13) + (1/13 - 1/16)]
    = 1/3[1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + 1/10 - 1/13 + 1/13 - 1/16]
    = 1/3[1 - 1/16]
    = 1/3[ (16 - 1)/16]
    = 1/3[ (15)/16]
    = 1 x 15/ 3 x 16
    = 5/16

    • More questions

    • 1. 
      A train 550 metres long is running with a speed of 55 km per hour. In what time will it pass a signal post?

    • Options
    • A. 30 sec
    • B. 24 sec
    • C. 42 sec
    • D. 36 sec
      • Discuss
    • 2. 
      95 3.7 ÷ 95 0.9989 = 95 ?

    • Options
    • A. 1.9
    • B. 3
    • C. 2.99
    • D. 2.7
      • Discuss
    • 3. 
      If the discount on a certain sum in 2 years at a certain rate is $ 150 and the interest in 3 years is $ 240. Find the sum and the rate of interest.

    • Options
    • A. $ 2400, 3 1 % 3
    • B. $ 2400, 4 1 % 3
    • C. $ 2200, 5 1 % 3
    • D. $ 2000, 3 1 % 3
      • Discuss
    • 4. 
      ❨ √625 x 14 x 11 ❩ is equal to:
      11 √25 √196

    • Options
    • A. 5
    • B. 6
    • C. 8
    • D. 11
      • Discuss
    • 5. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

    • Options
    • A. 3.5 years
    • B. 4 years
    • C. 4.5 years
    • D. 5 years
      • Discuss
    • 6. The ratio of expenditure and savings is 3 : 2 . If the income increases by 15% and the savings increases by 6% , then by how much percent should his expenditure increases?

    • Options
    • A. 25
    • B. 21
    • C. 12
    • D. 24
      • Discuss
    • 7. The average weight of boys in a class is 30 kg and the average weight of girls in the same class is 20kg. If the average weight of the whole class is 23.25 kg, what could be the possible strength of boys and girls respectively in the same class?

    • Options
    • A. 14 and 16
    • B. 13 and 27
    • C. 17 and 27
    • D. None of these
      • Discuss
    • 8. The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is

    • Options
    • A. Rs. 19.50
    • B. Rs. 19
    • C. Rs. 18
    • D. Rs. 18.50
      • Discuss
    • 9. The ratio of petrol and kerosene in the container is 3:2 when 10 liters of the mixture is taken out and is replaced by the kerosene, the ratio become 2:3. Then total quantity of the mixture in the container is:

    • Options
    • A. 25
    • B. 30
    • C. 45
    • D. cannot be determined
      • Discuss
    • 10. In a pot, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk, the pot would be full and ratio of milk and water would become 6 : 5. Find the capacity of the pot?

    • Options
    • A. 11 lit
    • B. 22 lit
    • C. 33 lit
    • D. 44 lit
      • Discuss

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