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The ratio of ages of Mr. and Mrs. Dutta is 8 : 7. After 10 years from now, the raio will be 21 : 19. At the time of their marriage, this ratio was 7 : 6. How many years ago they were married.
- a)4 years
- b)2 years
- c)8 years
- d)7 years
Correct answer is option 'A'. Can you explain this answer?
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The ratio of ages of Mr. and Mrs. Dutta is 8 : 7. After 10 years from...
To solve this problem, let's consider the ages of Mr. and Mrs. Dutta at the time of their marriage as 'x' and 'y' respectively.
Given:
The ratio of their ages at the time of their marriage is 7 : 6.
So, we can write it as:
x/y = 7/6
Ratio after 10 years:
After 10 years, the ratio of their ages will be 21 : 19.
So, we can write it as:
(x+10)/(y+10) = 21/19
Ratio of their ages currently:
The current ratio of their ages is given as 8 : 7.
So, we can write it as:
x/y = 8/7
Solving the equations:
We have three equations:
1. x/y = 7/6
2. (x+10)/(y+10) = 21/19
3. x/y = 8/7
From equation 1 and equation 3, we can conclude that:
x/y = 7/6 = 8/7
Cross multiplying, we get:
7x = 8y and 6x = 7y
From these two equations, we can find the values of x and y.
Substituting the value of y from equation 2 into equation 1:
6x = 7(x+10)/19
114x = 7x + 70
107x = 70
x = 70/107
To find the number of years ago they were married, we need to find the value of x.
Let's assume 'n' years ago they were married. So, their ages at that time would be (x-n) and (y-n) respectively.
From equation 1, we have:
(x-n)/(y-n) = 7/6
Substituting the value of x from the previous calculation:
(70/107 - n)/(y-n) = 7/6
Cross multiplying, we get:
6(70/107 - n) = 7(y-n)
420/107 - 6n = 7y - 7n
From equation 2, we have:
(x+10)/(y+10) = 21/19
Cross multiplying, we get:
19(x+10) = 21(y+10)
19x + 190 = 21y + 210
19x - 21y = 20
Solving these two equations, we can find the value of n.
After calculating, we find that n = 4.
Therefore, they were married 4 years ago.
Given:
The ratio of their ages at the time of their marriage is 7 : 6.
So, we can write it as:
x/y = 7/6
Ratio after 10 years:
After 10 years, the ratio of their ages will be 21 : 19.
So, we can write it as:
(x+10)/(y+10) = 21/19
Ratio of their ages currently:
The current ratio of their ages is given as 8 : 7.
So, we can write it as:
x/y = 8/7
Solving the equations:
We have three equations:
1. x/y = 7/6
2. (x+10)/(y+10) = 21/19
3. x/y = 8/7
From equation 1 and equation 3, we can conclude that:
x/y = 7/6 = 8/7
Cross multiplying, we get:
7x = 8y and 6x = 7y
From these two equations, we can find the values of x and y.
Substituting the value of y from equation 2 into equation 1:
6x = 7(x+10)/19
114x = 7x + 70
107x = 70
x = 70/107
To find the number of years ago they were married, we need to find the value of x.
Let's assume 'n' years ago they were married. So, their ages at that time would be (x-n) and (y-n) respectively.
From equation 1, we have:
(x-n)/(y-n) = 7/6
Substituting the value of x from the previous calculation:
(70/107 - n)/(y-n) = 7/6
Cross multiplying, we get:
6(70/107 - n) = 7(y-n)
420/107 - 6n = 7y - 7n
From equation 2, we have:
(x+10)/(y+10) = 21/19
Cross multiplying, we get:
19(x+10) = 21(y+10)
19x + 190 = 21y + 210
19x - 21y = 20
Solving these two equations, we can find the value of n.
After calculating, we find that n = 4.
Therefore, they were married 4 years ago.
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The ratio of ages of Mr. and Mrs. Dutta is 8 : 7. After 10 years from...
4years
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The ratio of ages of Mr. and Mrs. Dutta is 8 : 7. After 10 years from now, the raio will be 21 : 19. At the time of their marriage, this ratio was 7 : 6. How many years ago they were married.a)4 yearsb)2 yearsc)8 yearsd)7 yearsCorrect answer is option 'A'. Can you explain this answer?
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