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CTET Maths - Algebra

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6. I have one rupee coins, fifty paise coins and twenty five paise coins. The number of coins are in the ratio of 2.5 : 3: 4. If the total amount is 210 Rs. The number of one rupee coin is

  • Option : D
  • Explanation : (4) Let number of 1 Rs,50 paise and 25 paise coins be 2.5x, 3x and 4x, respectively. Value of 1 Rs coins = 1 x 2.5x= 2.5x Rs. Value of 50 paise coins = 0.50 x 3x. =1.5x Rs. Value of 25 paise coins = 0.25 x 4x. =lx Rs, Total value = 210 Rs. ⇒2.5x + 1.5x + 1x =210 => 5x = 210 ⇒X= 42 Thus, number of 1 Rs coins= 2.5x = 2.5 x 42 = 105
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7. Anita bought some pencils, erasers and graph papers from a stationary shop. If the ratio of the pencils and the erasers is the same as that of erasers and graph papers and she bought 10 pencils and 40 graph papers. Find the number of eraser bought by her.

  • Option : A
  • Explanation : Let number of eraser be x, then 10 : x = x : 40 ⇒ 10/x = x/40 ⇒ x 2= 40 × 10 = 400.⇒ x = 20
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8. Suppose, y varies as the sum of two quantities of which one varies directly as x and the other inversely as x.If y= 6 when x=4 and when x = 3, then the relation between x and y is

  • Option : A
  • Explanation : Let y = a + b, where a∝x and b∝1/x.
    Let a = K1x and b=K2/x.
    where K1 and K2 are constants.
    y = K1 x+ K2/x . .. (i).
    Given, y = 6 when x = 4.
    6 = K14 + K2/4.
    ⇒16K1 + K2 = 24 . .. (ii)
    Also,  when x = 3 .
    ⇒10/3 = 3K1 + K2/3
    ⇒9K1 + K2 = 10 . .. (iii)
    From Eqs. (i) and (ii), we get
    K1 = 2 and K2 = - 8.
    y=2x-8/x .
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9. Average of four numbers is 10.5. If three of these numbers be 4,9 and 13, find the fourth number.

  • Option : A
  • Explanation : Let fourth number be x. Average = Sum of numbers / Number of numbers ⇒ 10.5 = (4 + 9 + 13 + x) / 4 ⇒ 10.5 x 4 = 26 + x ⇒ 42-26=x ⇒ X= 16
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10. Average age of a group of five students is 14 yr. If a new student also admitted the group, new average age becomes 13 yr. Find the age of new student.

  • Option : D
  • Explanation : Average age of five students = 14 :. Sum of ages of five students = 14 x5 =70 Again, average age of six students = 13 :. Sum of ages of six students = 13 x 6 =78 Thus, age of new student = 78 - 70 = 8 yr
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