Linear Equation


  1. The sum of three consecutive odd numbers is 20 more than the first of these numbers.What is the middle number ?









  1. View Hint View Answer Discuss in Forum

    Let us assume the first Odd number is a.
    then 2nd odd number = a + 2
    and 3rd odd number = a + 4
    According to question,
    Sum of three consecutive odd numbers is 20 more than the first of these numbers;
    a + (a + 2) + (a + 4) = a + 20
    Solve the equation and get the answer.

    Correct Option: B

    Let us assume the first Odd number is a.
    then 2nd odd number = a + 2
    and 3rd odd number = a + 4
    According to question,
    Sum of three consecutive odd numbers is 20 more than the first of these numbers;
    a + (a + 2) + (a + 4) = a + 20
    ⇒ a + a + 2 + a + 4 - a = 20
    ⇒ 2a + 6 = 20
    ⇒ 2a + 6 = 20
    ⇒ 2a = 20 - 6
    ⇒ 2a = 14
    ⇒ a = 7
    The First odd number a = 7
    The second odd number = a + 2 = 7 + 2 = 9
    Second odd number is middle number = 9


  1. The sum of three consecutive multiples of 3 is 72. What is the largest number ?









  1. View Hint View Answer Discuss in Forum

    Method 1
    Let us assume the number be 3p , 3(p+1) and 3(p+2)
    According to question,
    3p + 3(p+1) + 3(p+2) = 72
    Solve the equation and find the answer.

    Method 2
    Let us assume the numbers P , P + 3 ,P+ 6
    According to Question,
    sum of three numbers = 72
    P + P + 3 + P + 6 = 72
    Solve the equation and find the answer.

    Correct Option: C

    Method 1
    Let us assume the number be 3p , 3(p+1) and 3(p+2)
    According to question,
    3p + 3(p+1) + 3(p+2) = 72
    ⇒ 3p + 3p + 3 +3p + 6 = 72
    ⇒ 9p +9 = 72
    ⇒ 9p = 72 - 9
    ⇒ 9p = 63
    ⇒ p = 63/9 = 7
    Largest number = 3(p + 2)
    Put the value of p in above equation.
    ⇒ Largest number = 3 x ( 7 + 2 )
    ⇒ Largest number = 3 x 9
    ⇒ Largest number = 27

    Method 2
    Let us assume the numbers P , P + 3 ,P+ 6
    According to Question,
    sum of three numbers = 72
    P + P + 3 + P + 6 = 72
    ⇒ 3P + 9 = 72
    ⇒ 3P = 72 - 9
    ⇒ 3P = 72 - 9
    ⇒ P = 63/3
    ⇒ P = 21
    So largest Number = P + 6 = 21 + 6 = 27



  1. The present ages of Vikas and Vishal are in the ratio 15:8. After ten years , their ages will be in the ratio 5:3. Find their present ages









  1. View Hint View Answer Discuss in Forum

    Method 1
    Let us assume the ratio factor is x.
    Therefor the present ages of Vikas and Vishal be 15x years and 8x years.
    After 10 years
    vikas's age = 15x + 10 and Vishal' age = 8x + 10
    According to question,
    (15x+10)/(8x+10) = 5/3
    solve the equation and get the answer.

    Method 2
    Let us assume the present age of Vikas = x years and Vishal's present year = y years
    According to question,
    Present age of Vikas/ Present age of Vishal = 15/8
    ⇒ x/y = 15/8
    ⇒ 8x = 15y
    ⇒ 8x - 15y = 0
    ⇒ x = 15y/8 .................................(1)
    After 10 years Vikash age = x + 10 and vishal age = y + 10
    Ratio of age after 10 years = 5/3
    (x + 10)/(y + 10) = 5/3
    solve the equation and get the answer.



    Correct Option: A

    Method 1
    Let us assume the ratio factor is x.
    Therefor the present ages of Vikas and Vishal be 15x years and 8x years.
    After 10 years
    vikas's age = 15x + 10 and Vishal' age = 8x + 10
    According to question,
    (15x+10)/(8x+10) = 5/3
    ⇒ 3(15x + 10) = 5(8x + 10)
    ⇒ 45x + 30 = 40x + 50
    ⇒ 5x =20
    ⇒ x = 20/5
    ⇒ x = 4
    Therefore Present age of Vikas = 15x = 15 x 4 = 60 years
    and Present age of Vishal = 8x = 8 x 4 = 32 years

    Method 2
    Let us assume the present age of Vikas = x years and Vishal's present year = y years
    According to question,
    Present age of Vikas/ Present age of Vishal = 15/8
    ⇒ x/y = 15/8
    ⇒ 8x = 15y
    ⇒ 8x - 15y = 0
    ⇒ x = 15y/8 .................................(1)
    After 10 years Vikash age = x + 10 and vishal age = y + 10
    Ratio of age after 10 years = 5/3
    (x + 10)/(y + 10) = 5/3
    ⇒ 3(x + 10) = 5(y + 10)
    ⇒ 3x + 30 = 5y + 50
    ⇒ 3x - 5y = 50 - 30
    ⇒ 3x - 5y = 20 ................................(2)
    Put the value of x from equation (1) in above equation (2).
    ⇒ 45y/8 - 5y = 20
    ⇒ 45y - 40y = 20 x 8
    ⇒ 5y = 20 x 8
    ⇒ y = 4 x 8 = 32
    Put the value of Y in equation (1)
    x = 15 x 32/8 = 15 x 4 = 60

    Therefore Present age of Vikas = x = 60 years
    and Present age of Vishal = y = 32 years


  1. 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









  1. View Hint View Answer Discuss in Forum

    Let use assume the fixed charge = a
    and charge for 1 km = b
    According to question,
    for 10 KM journey charge paid = 85
    a + 10 x b = 85
    a + 10b = 85 .........................(1)
    for 15 KM journey charge paid = 120
    a + 15b = 120.........................(2)
    Solve the equation (1) and (2) to get the answer.

    Correct Option: B

    Let use assume the fixed charge = a
    and charge for 1 km is = b
    According to question,
    for 10 KM journey charge paid = 85
    a + 10 x b = 85
    a + 10b = 85 .........................(1)
    for 15 KM journey charge paid = 120
    a + 15b = 120.........................(2)
    Subtract the equation (1) from equation (2). we will get,
    a + 15b - a - 10b = 120 - 85
    5b = 35
    b = 7
    Put the value of b in equation (1). we will get
    a + 10 x 7 = 85
    a = 85 - 70
    a = 15
    Charges for 25 km = a + 25 x b
    Put the value of a and b in above equation.
    Charges for 25 km =15 + 25 x 7 = 15 + 175 = 190
    Charges for 25 km =190



  1. 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









  1. View Hint View Answer Discuss in Forum

    Let us assume the ratio term is r.
    then the number will be 3r and 4r.
    According to question,
    (4r)2 + 224 = 8 x (3r)2
    Solve the equation and find the answer.

    Correct Option: C

    Let us assume the ratio term is r.
    then the number will be 3r and 4r.
    According to question,
    (4r)2 + 224 = 8 x (3r)2
    16r2 + 224 = 8 x 9r2
    16r2 + 224 = 72r2
    72r2 - 16r2 = 224
    56r2 = 224
    r2 = 224/56
    r2 = 4
    r = 2

    First number = 3r = 3 x 2 = 6
    Second number = 4r = 4 x 2 = 8