Wednesday, 3 February 2016

MATHS (SOLVED IN STEPS) Problems on Age - (Page -4)

MATHS (SOLVED IN STEPS)
Problems on Age - (Page -4)
25.If 6 years are subtracted from the present age of Ajay and the remainder is divided by 18, then the present age of Rahul is obtained. If Rahul is 2 years younger to Denis whose age is 5 years, then what is Ajay 's present age?
A.50     B.60     C. 55   D.62
Answer : Option B
Explanation :
Present age of Denis = 5 years
Present age of Rahul = 5-2 = 3
Let the present age of Ajay = x
Then (x-6)/18 = present age of Rahul = 3
=> x- 6 = 3×18 = 54
=> x = 54 + 6= 60

26.The ratio of the age of a man and his wife is 4:3. At the time of marriage the ratio was 5:3 and After 4 years this ratio will become 9:7. How many years ago were they married
A.8     B.10    C. 11   D.12
Answer : Option D
Explanation :
Let the present age of the man and his wife be 4x and 3x respectively.
After 4 years this ratio will become 9:7
=> (4x + 4)/ (3x + 4) = 9/7
=> 28x + 28 = 27x + 36
=> x = 8
=> Present age of the man = 4x = 4×8 = 32
Present age of his wife = 3x = 3×8 = 24
Assume that they got married before t years.
Then (32 – t) / (24 – t) = 5/3
=> 96 – 3t = 120 – 5t
=> 2t = 24
=> t = 24/2 = 12

27.The product of the ages of Syam and Sunil is 240. If twice the age of Sunil is more than Syam's age by 4 years, what is Sunil's age?
A.16     B.14    C. 12   D.10
Answer : Option C
Explanation :
Let the age of Sunil = x and age of Syam = y.
Then xy = 240 ---(1) 2x = y + 4
=> y = 2x – 4
=> y = 2(x – 2) ---(2)
Substituting equation (2) in equation (1). We get x × 2(x-2) = 240
=> x (x-2) = 240/2
=> x (x -2) = 120 ---(3)
We got a quadratic equation to solve.  Always time is precious and objective tests measures not only how accurate you are but also how fast you are. We can either solve this quadratic equation in the traditional way. But more easy way is just substitute the values given in the choices in the quadratic equation (equation 3 ) and see which choice satisfy the equation.
  Here the option A is 10. If we substitute that value in the quadratic equation, x(x-2) = 10 × 8 which is not equal to 120
Now try option B which is 12. If we substitute that value in the quadratic equation, x(x-2) = 12 × 10 = 120.
See, we got that x = 12.
Hence Sunil's age = 12

28.One year ago, the ratio of Sooraj's and Vimal's age was 6: 7 respectively. Four years hence, this ratio would become 7: 8. How old is Vimal?
A.32    B.34    C. 36   D.38
Answer : Option C
Explanation :
Let take the age of Sooraj and Vimal , 1 year ago as 6x and 7x respectively. Given that, four years hence, this ratio would become 7: 8.
=> (6x + 5)/(7x + 5) = 7/8
=> 48x + 40 = 49x + 35
=> x = 5
Vimal's present age = 7x + 1 = 7×5 + 1 = 36

29.The total age of A and B is 12 years more than the total age of B and C. C is how many year younger than A?
A.10  B.11   C. 12   D.13
Answer : Option C
Explanation :
Given that A+B = 12 + B + C
=> A – C = 12 + B – B = 12
=> C is younger than A by 12 years

30.Sachin's age after 15 years will be 5 times his age 5 years back. Find out the present age of Sachin?
A.10  B.11   C. 12   D.13
Answer : Option A
Explanation :
Let the present age of Sachin = x
Then (x+15) = 5(x-5)
=> 4x = 40
=> x = 10

31.Sandeep's age after six years will be three-seventh of his father's age. Ten years ago the ratio of their ages was 1 : 5. What is Sandeep's father's age at present?
A.30  B.40 C. 50   D.60
Answer : Option C
Explanation :
Let the age of Sandeep and his father before 10 years be x and 5x respectively. Given that Sandeep's age after six years will be three-seventh of his father's age
=> x + 16 = (3/7)(5x + 16)
=> 7x + 112 = 15x + 48
=> 8x = 64
=> x = 8

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