21. Five years ago, the ratio of the ages of a father and his son was 5 : 3. Which of the following cannot be the ratio of their ages 10 years from now?
     
पांच वर्ष पहले, एक पिता और उसके बेटे की आयु का अनुपात 5 : 3 था। अब से 10 वर्ष के बाद निम्नलिखित में से कौन सा उनकी आयु का अनुपात नहीं हो सकता है?

Option “D” is correct.

Given: 

The ratio of father and son 5 years ago = 5 ∶ 3

Calculation:

Let the age of father and son, 5 years ago be 5x and 3x respectively

Then, Present age of Father = 5x + 5

The present age of son = 3x + 5

After 10 years,

The age of father = 5x + 5 + 10 = 5x + 15

The age of son = 3x + 5 + 10 = 3x + 15 

Ratio of father and son = (5x + 15)/(3x + 15)

Checking the given option one by one

Option 1, 

(5x + 15)/(3x + 15) = 3/2

⇒ 10x + 30 = 9x + 45

⇒ x = 15

It gives positive value so it can be the ratio of their age

Option 2,

(5x + 15)/(3x + 15) = 8/7

⇒ 35x + 105 = 24x + 120

⇒ x = 15/11

It gives positive value so it can be the ratio of their age

Option 3,

(5x + 15)/(3x + 15) = 6/5

⇒ 25x + 75 = 18x + 90

⇒ x = 15/7

It gives positive value so it can be the ratio of their age

Option 4,

(5x + 15)/(3x + 15) = 7/3

⇒ 15x + 45 = 21x + 105

⇒ x = -60/6 = -10

Age can not be in negative

∴ 7 ∶ 3 can not be the ratio of their ages after 10 years

22. Three years ago, the average age of a husband, wife, and child was 26 years, and that of the wife and the child, 5 years ago, was 20 years. The present age of the husband is:

तीन वर्ष पहले, पति, पत्नी और बच्चे की औसत आयु 26 वर्ष थी, और 5 वर्ष पहले, पत्नी और बच्चे की 20 वर्ष थी। पति की वर्तमान आयु कितनी है?

Option “C” is correct.

Given:

Three years ago, the average age of a husband, wife, and child was 26 years

Five years ago, the average age of wife and the child = 20

Formula:

Average = Sum of all observations/Total number of observations

Calculation:

Three years ago, sum of age of husband, wife and child = 3 × 26 = 78 years

Present sum of age of husband, wife and child = 78 + 9 = 87 years

Five years ago, sum of age of wife and child = 2 × 20 = 40 years

Present sum of age of wife and child = 40 + 10 = 50

∴ Present age of husband = 87 – 50 = 37 years

23. The ratio of the present ages of Meera and Sheela is 9 : 5. After 8 years Sheela would reach the present age of Meera. What is the present ages (in years) of Sheela?

मीरा और शीला की वर्तमान आयु का अनुपात 9 : 5 है। 8 वर्ष बाद शीला, मीरा की वर्तमान आयु तक पहुंच जाएगी। शीला की वर्तमान आयु (वर्षों में) क्या है?

Option “B” is correct.

Given:

The ratio of the present ages of Meera and Sheela is 9 : 5.

Calculation:

Let the present ages of Meera and Sheela be 9x & 5x respectively.

According to question,

⇒ (5x + 8) = 9x

⇒ 4x = 8

⇒ x = 2

⇒ 5x = 10

∴ The present age of Sheela is 10 years.

24. The present ages of A and B are in the ratio 15 : 8. After 8 years their ages will be in the ratio 17 : 10. What will be the ratio of the ages of A and B after 10 years from now?

A और B की वर्तमान आयु का अनुपात 15 : 8 है। 8 वर्षों के बाद उनकी आयु का अनुपात 17 : 10 होगा। अभी से 10 वर्षों के बाद A और B की आयु का अनुपात क्या होगा?

Option “C” is correct.

Calculation:

Let present age of A = 15x years ad B = 8x years

According to ques,

⇒15x+88x+8=1710

⇒150x+80=136x+136

⇒14x=136−80=56

⇒x=56/14=4

∴ The ratio of the ages of A and B after 10 years from now = 15×4+10 /8×4+10

=7042=5:3

∴ Required  ratio = 5 : 3

25. The ratio of ages of A and B, 4 years ago, was 5 : 7. The ratio of their ages after 4 years from now will be 7 : 9. What will be the ratio of ages of A and B after 12 years from now?

4 वर्ष पहले A और B की आयु का अनुपात 5 : 7 था। अब से 4 वर्ष बाद उनकी आयु का अनुपात 7: 9 होगा। अब से 12 वर्ष बाद A और B की आयु का अनुपात क्या होगा?

Option “C” is correct.

Given:

The ratio of ages of A and B 4 years ago = 5 : 7

The ratio of ages of A and B 4 years from now = 7 : 9

Calculation:

Let the constant be x

Age of A and B 4 years ago = 5x and 7x

According to question:

⇒ (5x + 8) / (7x + 8) = 7 / 9

⇒ 45x + 72 = 49x + 56

⇒ 4x = 16

⇒ x = 4

Present age of A and B =

Present age of A = 5× 4 = 20 + 4 = 24

Present age of B = 7 × 4 = 28 + 4 = 32

A’s age after 12 years = 24 + 12 = 36

B’s age after 12 years = 32 + 12 = 44

Ratio of A’s age after 12 years : B’s age after 12 years = 9 : 11

26. Two years ago, Ritu was three times as old as her daughter and two years hence, twice her age will be equal to five times that of her daughter. What is the sum of the present ages of Ritu and her daughter? 

दो वर्ष पूर्व, रितु अपनी बेटी से तीन गुनी बड़ी थी और दो वर्ष बाद, उसकी आयु का दो गुना उसकी बेटी की आयु के पाँच गुना के बराबर होगा। रितु और उसकी बेटी की वर्तमान आयु का योग क्या है? 

Option “C” is correct.

Let, Ritu’s daughter age two years ago be x and Ritu’s age be 3x.

Ritu’s age 2 year hence = 3x + 2 + 2 = 3x + 4

Ritu’s daughter age 2 year hence = x + 2 + 2 = x + 4

Given that,

⇒ 5(x + 4) = 2 × (3x + 4)

⇒ 5x + 20 = 6x + 8

⇒ 12 = x

∴ The sum of the present ages of Ritu and her daughter = (x + 2) + (3x + 2) = 4x + 4 = 4 × 12 + 4 = 52 years.

27.Mr. and Mrs. Das married 9 years ago when the age of Mrs. Das is 20% less than Mr. Das. Six years hence, the age of Mrs. Das is only 12.5% less than Mr. Das. Now they have six children including single, twin and triplet and the ratio of their age is 2 ∶ 3 ∶ 4. What can be the maximum possible value for present age of family?

श्रीमान और श्रीमती दास की शादी 9 वर्ष पहले हुई थी जब श्रीमती दास की आयु श्री दास से 20% कम है| 6 वर्ष बाद श्रीमती दास की आयु श्रीमान दास से केवल 12.5% कम है। अब उनके एकल, जुड़वां और तीन बच्चों सहित छह बच्चे हैं और उनकी आयु का अनुपात 2 : 3 : 4 है। परिवार की वर्तमान आयु के लिए अधिकतम संभव मान क्या हो सकता है?

Option “C” is correct.

Calculation:

Let the age of Mr. Das be x and Mrs. Das be y

9 years ago the age of Mrs. Das was 20% less,

⇒ x−9/y−9=5/4

⇒ 4x – 5y = -9      —-(i)

And 6 years hence the age of Mrs. Das is 12.5% less,

⇒ x+6/y+6=8/7

⇒ 7x – 8y = 6      —-(ii)

By equation (i) and (ii), we get

⇒ x = 34 years and y = 29 years

Now the maximum age of any child must be less than 9 years so their age can be 2, 3 and 4 years or 4, 6 and 8 years

∴ The maximum possible age of family = 34 + 29 + (1 × 4 + 2 × 6 + 3 × 8) = 103 years

28. Four years ago, the ratio of age of A and B was 3:4, Average of the present age of A, B and C is 26 years. C is 11 years younger than B. What is the present age of B?

चार वर्ष पहले A और B की आयु का अनुपात 3 : 4 था, A, B और C की वर्तमान आयु का औसत 26 वर्ष है। C, B से 11 वर्ष छोटा है। B की वर्तमान आयु क्या है?

Option “C” is correct.

Ratio of age of A and B four years ago was 3 ∶ 4

Let the age of A and B four years ago be 3x and 4x respectively

∴ Present age of A = 3x + 4

Present age of B = 4x + 4

C is 11 years younger than B

Present age of C = 4x – 7

Average age of A, B and C is 26 years

∴ Sum of ages of A, B and C = 26 × 3 = 78

⇒ (3x + 4) + (4x + 4) + (4x – 7) = 78

⇒ 11x + 1 = 78

⇒ x = 7

Present age of B = 4x + 4 = (4 × 7) + 4 = 32

∴ Present age of B is 32 years

29. The average age of 24 students in a class is 15.5 years. The age of their teacher is 28 years more than the average of all twenty-five. What is the age of the teacher in years?

एक कक्षा में 24 छात्रों की औसत आयु 15.5. वर्ष है। उनके अध्यापक की आयु सभी 25 की औसत आयु से 28 वर्ष अधिक है। अध्यापक की आयु वर्ष में क्या है?

Option “C” is correct.

Given:

The average age of 24 students in a class is 15.5 years. The age of their teacher is 28 years more than the average of all twenty-five. 

Formula Used:

average = sum of observation/number of observation

Calculation:

Average age of 24 students in the class = 15.5 years

⇒ Total age of 24 students = 24 × 15.5 = 372 years

Let age of teacher = x years and average age of all 25 = 372+x/25

⇒ x = 28 + 372+x/25

⇒ 25x – x = 700 + 372

⇒ x = 1072/24=134/3

Thus, age of teacher = 44 2/3 years

30. The sum of the age of a father and his son is 80 years now, 5 years ago their age was in the ratio of 5 : 2. The ratio of the age of father and son after 5 years will be?

एक पिता और उसके पुत्र की आयु का योग अब 80 वर्ष है, 5 वर्ष पहले उनकी उम्र 5: 2 के अनुपात में थी। 5 वर्ष के बाद पिता और पुत्र की आयु का अनुपात होगा?

Given:

Father + son present age = 80 years

Father: son, 5 years ago = 5 : 2

Calculation:

Let the age of son 5 years ago = 2x

The age of father 5 years ago = 5x

⇒ 2x + 5 + 5x + 5 = 80

⇒ 7x + 10 = 80

⇒ 7x = 70

⇒ x = 10

Father present age = 5 × 10 + 5 = 55 years

Son present age = 2 × 10 + 5 = 25 years

After 5 years

⇒ ratio = 60 : 30

⇒ 2 : 1

∴ ratio of father and son after 5 years is 2 : 1.

 

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131 thoughts on “Problems on Ages”

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