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Age Problems and answers
1.The Present age of a father is 3 years more than three times the age of his son. Three years hence, father’s age will be 10 years more than twice the age of the son .Find the present age of the fatther
Let the son’s present age be x age years,
then fathers present age = (3x +3) years
(3x+3 + 3) = 2 (x +3) + 10 => 3x + 6 => 2x + 16
x = 10
Hence father present age = (3x +3) = 3 * 10 + 3= 33 years
2.One year, the ratio fo Gaurav’s and sachin age was 6 :5 respectively.Four year hence this ratio would become 7:8 .How old is sachin ?
Let Guarav’s and sachin ages one year ago be 6x and 7x respectivley ,Then
Guarav age 4 years hence = ( 6x +1+4 = 6x + 5
Guarav age 4 years hence = 7x + 1 + 4 = 7x +5
6x+5/7x + 5 = 7/8 => 8 ( 6x + 5) = 7 (7x + 5)
48x + 40 = 49 x + 35
x = 5
Hence, sachin present age = 7x +1 = 36 years
3.The ages of two persons differ by 16 years.If 6 years ago, the elder one be 3 times as old as the younger one,Find the present age
Let the age of the younger person be x years
Then age of the elder person = (x + 16 ) years
3 (x -6 ) = x+ 16–6
=> 3x -18 = x +10
=>2x = 28
x = 14
Hence their present ages are 14 years and 30 years
4
Sachin is younger than rahul by 4 years.If their ages are in the respective ratio of 7 : 9 .How old is yours
Let Rahuls age be x years.Then sachin age = (x -7) years
x -7 /x = 7/9
9x -63 = 7x
2x = 63
x = 31.5
Hence, Sachin age = (x — 7) = 24.5 years
5 six years ago, the ratio of the ages of kunal and sagar was 6:5 Four years hence the ratio of the ages will be 11:10 .what is sagar age at present ?
Let the ages of kunal and sagar 6 years ago be 5x and 6x years respectively
( 6x +6 +4)/5x + 6+ 4 = 11/10
10 (6x + 10 ) = 11( 5x + 10 )
5x = 10
x= 2
Sagar present age = ( 5x + 6 ) = 16 years
6 Eighteen years ago, afather was three times as old as his son.Now the father is only twice as old as his son.Then the sum of the present ages of the son and the father is
Let the present ages of the father and son be 2x and x years
(2x — 18 ) = 3 (x -18 ) => x= 36
Required sum = 2x + x = 3x = 108 years
7The sum of the present ages of a father and his is 60 years.Six years ago , Fathers age was five times the age of the son.After 6 years, son’s age will be
Let the present ages of son and father be x and 60 -x years respectively
4x +1 + 6 — ([x + 1 ) + 6] = 9
3x = 9
x =3
Therefore ratio = (4x + 1) : (x + 1) = 13 : 4
8 Tanya grandFather was 8 times older to her 16 year ago.He would be 3 times of her 8 years from now.Eight years ago what was the ratio of Tanya age to that of her grand father
16 years ago, Let T = xyears and G = 8x years
After 8 years from now T = (x+ 16 + 8 ) years
G= 8x + 16 + 8 years
therefore 8x + 24 = 3 ( x + 24 ) = > 5x = 48
8 years ago => T/g = x +8/8x + 8 = 48/5 + 8/8 * 48/5 + 8
= 88/424 = 11/53
9 Rajan got married 8 years ago.HIs present age is 6/5 times his age at the time of his marriage .Rajan sister was 10 years younger to hinm at the time at the time of his marriage .The age of rajan’s sister is
Let Rajan present age be x years ,
Then his age at the time of marraige = ( x-8 )
x = 6/5(x — 8)
5x = 6x — 48
= > x =48
Rajan sister age at the time of marriage ( x-8 -10 )= x — 18 = 30 years
Rajan ‘s sister’s present age = 30 + 8 = 38 years
10.A father said to his son” I was as old as you are at present at the time of your birth .If the father’s age is 38 years now,the son’s
age five year back was
Let the son’s present age be x years = > then (38 — x) = x
2x = 38 x =19
Son age 5 years back = 19 -5 years = 14 years
ratios Problems and answers
1
A bag contains 50p, 25p and 10 p coins in the ratio 5:9:4 amounting to Rs 206 .Find the number of coins of each type
Let the number of 50 p, 25p and 10 p coins be 5x, 9x, and 4x respectively
then 5x/2+9x/4+4x/10 = 206
50x + 45x + 8x =4120
103x = 4120
x = 20
Number of 50 p coins = 5*40 = 200
Number of 25p coins = 9* 40 = 360
Number of 10 p coins = 4 * 40 = 160
2
A mixture contains alcohol and water in the ratio 4:3 If 5 litres of water is added to the mixture, the ratio become 4:5 .Find the quantity of alcohol in the given mixture
Let the quantity of alchol and water be 4x litres and 3x litres respectively then
4x/3x+5 = 4/5
20 x = 4(3x + 5)
8x = 20
x = 2.5
quantity of alochol = 4 * 2.5 litres = 10 litres
3
Salaries of Ravi and sumit are in the ratio of 2:3 .If the salary of each is increased by Rs 4000. the new ratio becomes 40 : 57 what is sumit present salary ?
Let the original salaries of Ravi and sumit be 2x and 3x respectively then
2x+4000/3x+4000 = 40/57
57(2x+ 4000) = 40(3x +4000)
6x = 68000 3x = 34000
sumit present salary = (3x + 4000) = Rs (34000 + 4000)
= Rs 38,000
4 The salaries of A , B, C are in the ratio 2:3:5 . If the increments of 15%, 10 % , and 20 % are allowed respectively in their salaries, then what will be the new ratio of their salaries
Let A = 2K B = 3k c = 5k
A ‘S new salary = 115/100 of 2k= (115/100 * 2k ) = 23 k/10
B ‘S new salary = 110/100 of 3k= (110/100 * 3k ) = 33 k/10
C’s new salary = 120/100 of 5 k = (120/100 * 5k ) = 6k
New ratio = 23k/10 : 33k/10 :6k = 23:33: 60
5 Two numbers are in the ratio of 3:5 . If 9 is substracted from each , the new numbers are in the ratio 12 : 23. The smaller number is
Let the numbers be 3x and 5x then 3x-9 /5x-9 =12/23
23(3x -9) = 12 (5x — 9)
9x= 99 => x = 11
6 If Rs 1210 were divided among A, B,C so that A :B = 5:4 and B : C => 9 : 10 Then gets
A : B = 5 : 4 B :C = 9 :10 = (9 * 4/9 ) : (10 * 4/9 ) = 4 : 40 /9
A :B:C = 5: 4 : : 40 /9 = 45 : 36 : 40
sum of ratio terms = (45 + 36 + 40 ) = 121
therefore C’;s share = RS (1210 * 40 /121)= Rs 400
7 An alloy is to contain copper and zine in the ratio 9 : 4 .the zine required to be melted with 24 kg of copper is
Let the required quantity of copper be x kg
then 9 :4 : : 24 : x => 9x = 4* 24 x = 4 * 24 /9 = 10 2/3
Hence the required quantity of copper us 10 2/3 kg
8 The ratio of the number of boys and girls in a school is 3:2 .If 20 % of the boys and 25 % of the girls are scholarship holders, what percentage of the students does not get the scholarhip
Let boys = 3x and girls = 2x
NUMBER of the who do not get scholarship
= (80 % of 3x ) + (75 % of 2x)
=80 /100 * 3x + 75/100 * 2x
= 39x/10
Required percentage = (39x/10 * 1/5* 100)% = 78 %
9 Zinc and copper are melted together in the ratio 9 :11 what is the weight of melted mixture . If 28.8 kg of zinc has been consumed in it ?
For 9 kg zinc, mixture melted = (9 +11) kg
For 28.8 kg zinc, mixture melted= (20 /9 * 28.8 ) kg = 64 kg
10 The sum of Rs 53 is divided among A , B, C in such a way that A gets Rs 7 more than what B gets and B gets Rs 8 more than what C gets . The ratio of their shares is :
Suppose C gets Rs x then B gets Rs ( x + 8 )
A gets Rs ( x + 15 )
Then x + ( x+ 8 )+ x + 15 = 53
x = 10
therefore A :B :C = (10 + 15) : (10 + 8) : 10
= 25 : 18 : 10
