The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.
45) A grandfather is ten times older than his granddaughter. He is also 54 years older than her. Find their present ages.
46. Amina thinks of a number and subtracts 5÷2from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?
47. Fifteen years from now Ravi’s age will be four times his present age. What is Ravi’s present age?
48. The number of boys and girls in a class are in the ratio 7:5. The number of boys is 8 more than the number of girls. What is the total class strength?
49. Three consecutive integers add up to 51. What are these integers?
50. The sum of three consecutive multiples of 8 is 888. Find the multiples.
Answers
Answer:
The ratio of Hari's and Harry's present ages is 5:7
So, let their ages be 5x and 7x
After 4 years their ages will be in ratio 3:4
Therefore,(5x+4)/(7x+4)=3/4
or, 4(5x+4)=3(7x+4)
or, 20x+16=21x+12
or, 16−12=21x−20x
or, 4=1x
or, x=4
Therefore, present age of Hari = 5x=(5×4)=20 years.
Present age of Harry =7x=(7×4)=28 years
The sum of their age is 28+20=48years
Let the three consecutive multiples of 8 be x, x+8 and x+ 16
According to question,
⇒ x+x+8+x+16 = 888
⇒ 3x+24 = 888
⇒ 3x+ 24-24 = 888 -24 [Subtracting 24 from both sides]
⇒ 3x = 864
⇒ 3x/3 = 864/3 [Dividing both sides by 3]
⇒ x= 288
Hence, first multiple of 8 = 288,
second multiple of 8 = 288 + 8 = 296 and
third multiple of 8 = 288 + 16 = 304.
Let the three consecutive integers be x, x+1 and x+2
According to the question,
⇒ x+x+1+x+2 = 51
⇒ 3x+ 3 = 51
⇒ 3x+3-3 = 51-3 [Subtracting 3 from both sides]
⇒ 3x = 48
⇒ 3x/3 = 48/3 [Dividing both sides by 3]
⇒ x= 16
Hence, first integer = 16,
second integer = 16 + 1 = 17 and
third integer = 16 + 2 = 18.
Let the number of girls be x
Then, the number of boys = x+ 8
According to the question,
⇒ (x+8)/x = 7/5
⇒5(x+8) = 7x
⇒ 5x+ 40 = 7x
⇒ 5x- 7x= -40
[Transposing 7x to L.H.S. and 40 to R.H.S.]
⇒-2x = -40
⇒ -2x/-2 = -40/-2 [Dividing both sides by -2]
⇒x= 20
Hence the number of girls = 20 and number of boys = 20 + 8 = 28.
Let Ravi’s present age be x years.
After fifteen years, Ravi’s age = 4x years.
Fifteen years from now, Ravi’s age = (x+15) years.
According to question,
⇒4x = x+ 15
⇒4x - x= 15 [Transposing x to L.H.S.]
⇒ 3x = 15
⇒ 3x/3 = 15/3 [Dividing both sides by 3]
⇒ x= 5 years
Hence, Ravi’s present age be 5 years.
Let Amina thinks of a number x.
According to the question, 8(x-5/2) = 3x
⇒ 8x - (8×5)/2 = 3x
⇒8x -4×5 = 3x
⇒8x-20 = 3x
⇒ 8x-3x = 20
⇒ 5x= 20
⇒x = 20/5 = 4
Hence, the number is 4.
Let present age of granddaughter be x years.
Therefore, Grandfather’s age = 10x years
According to question, 10x = x +54
⇒ 10x-x = 54
⇒ 9x = 54
⇒ x = 54/9 = 6 years
Hence, granddaughter’s age = 6 years and grandfather’s age = 10×6 = 60 years.