71. A’s age 6 years hence will be four-fifth of the present age of B, B’s present age is one-fourth of the C’s age 12 years hence. A’s age after 4 years is one-eighth of the D’s age after 4 years. If the sum of ages of A, B, C and D is 145 years, then what is the present age of B?

6 वर्ष के बाद A की आयु B की वर्तमान आयु के चार-पाँचवें(4/5) वर्ष होगी, B की वर्तमान आयु 12 वर्ष के बाद C की आयु की एक-चौथाई(1/4) है। 4 वर्ष के बाद A की आयु D की आयु का आठवाँ(1/8) भाग है। यदि A, B, C और D की आयु का योग 145 वर्ष है, तो B की वर्तमान आयु कितनी है?

A. 15 years
B. 12 years
C. 18 years
D. 9 years
E. None of these

A+6=4/5B

5A+30=4B

B=1/4*(C+12)

4B=C+12

5A+30=C+12

C=5A+18

A+4=1/8(D+4)

8A+32=D+4

D=8A+28

A+B+C+D=145

A+(5A+30)/4+5A+18+8A+28=145

4A+5A+30+20A+32A+72+112=145*4

61A=366

A=6

B=5(6)+30/4=60/4=15 years

72. Ratio of present age of Satish and Raju is 7: 6. Sum of the present age of Sweta and Satish is 54. Anu is 4 years younger than Raju. Average of present ages of Raju, Anu and Sweta is 23 1/3 years. Find the difference of Sweta and Anu’s age.

सतीश और राजू की वर्तमान आयु का अनुपात 7: 6 है। स्वेता और सतीश की वर्तमान आयु का योग 54 है। अनु, राजू से 4 वर्ष छोटी है। राजू, अनु और स्वेता की वर्तमान आयु का औसत 23 1/3 वर्ष है। स्वेता और अनु की आयु का अंतर ज्ञात करें।

A. 2
B. 4
C. 6
D. 8
E. None of these

Option “C” is correct.

Satish = 7x and Raju = 6x

Anu = 6x – 4 and Sweta + 7x = 54

Sweta = 54 – 7x

(6x + 6x – 4 + 54 – 7x)/3 = 23 1/3

=> x = 4

Swetha = 54 – 7x = 26 years

Anu = 6x – 4 = 20 years

Required difference = 26 – 20 = 6 years

73. The ratio of age of A, 3 years ago and the age of B, 5 years hence is 5: 7. 6 years hence, the ratio of age of A and B is in the ratio of 17: 18. Find the present age of C, if B is 8 years elder than C?

3 वर्ष पहले, A की आयु और 5 वर्ष बाद, B की आयु का अनुपात 5: 7 है। 6 वर्ष बाद, A और B की आयु का अनुपात 17: 18 है। C की वर्तमान आयु ज्ञात कीजिए, यदि B, C से 8 वर्ष बड़ा है?

A. 24 years
B. 22 years
C. 20 years
D. 26 years
E. None of these

Option “B” is correct.

The ratio of age of A, 3 years ago and the age of B, 5 years hence = 5: 7 (5x, 7x)

6 years hence, the ratio of age of A and B is in the ratio = 17: 18

According to the question,

= > (5x + 3 + 6) / (7x + 1) = (17/18)

= > (5x + 9) / (7x + 1) = (17/18)

= > 90x + 162 = 119x + 17

= > 29x = 145

= > x = 5

Present age of B = 7x – 5 = 35 – 5 = 30 years

Present age of C = 30 – 8 = 22 years

74. The ratio of age of P, 5 years ago to the age of Q, 6 years ago is 2: 3. The sum of the present age of P, Q and R together is 84 years. Find the present age of S, if S is 5 years elder than P and the age of R, 5 years hence is 28 years?

5 वर्ष पहले P की आयु से 6 वर्ष पहले Q की आयु का अनुपात 2: 3 है। P, Q और R की वर्तमान आयु का योग 84 वर्ष है। S की वर्तमान आयु ज्ञात कीजिए, यदि S, P से 5 वर्ष बड़ा है और 5 वर्ष बाद R की आयु 28 वर्ष है?

A. 28 years
B. 32 years
C. 30 years
D. 35 years
E. None of these

Option “C” is correct.

The ratio of age of P, 5 years ago to that of the age of Q, 6 years ago = 2: 3

The sum of the present age of P, Q and R together = 84 years

2x + 5 + 3x + 6 + 23 = 84

5x = 84 – 11 – 23 = 50

5x = 50

x = 10

The present age of P = 2x + 5 = 25 years

The present age of S = P + 5 = 25 + 5 = 30 years

75. The ratio of the present age of Ravi and Dinesh is 4 : x. Ravi is 6 years younger than Prem. Prem’s age after 4 years will be 34 years. The difference between the Dinesh and Ravi’s age is the same as the present age of Prem. What should come in place of x?

रवि और दिनेश की वर्तमान आयु का अनुपात 4: x है। रवि, प्रेम से 6 वर्ष छोटा है। 4 वर्ष के बाद, प्रेम की आयु 34 वर्ष होगी। दिनेश और रवि की आयु के बीच का अंतर प्रेम की वर्तमान आयु के समान है। x के स्थान पर क्या आना चाहिए?

A. 8
B. 7
C. 9
D. 10
E. None of these

Option “C” is correct.

Prem’s present age = 34 – 4 = 30 years

Ravi = Prem – 6 = 30 – 6 = 24 years

Dinesh’s age – Ravi’s age = Prem’s age

Dinesh’s present age – 24 = 30

Dinesh’s present age = 54 years

4’s = 24

1’s = 6

x = 54 / 6 = 9

76. The sum of the present age of A and B together is equal to the sum of the present age of B and C together. The present age of D is 28 years and B is 8 years younger than A. Find the present age of C, if the average age of A, B, C and D together is 20 years?

A और B की वर्तमान आयु का योग, B और C की वर्तमान आयु के योग के बराबर है। D की वर्तमान आयु 28 वर्ष है और B, A से 8 वर्ष छोटा है।C की वर्त्तमान आयु ज्ञात करें यदि A, B, C और D की औसत आयु एक साथ 20 वर्ष है?

A. 18 years
B. 22 years
C. 20 years
D. 24 years
E. None of these

Option “C” is correct.

The sum of the present age of A and B together = The sum of the present age of B and C together

A + B = B + C

A = C

Let the present age of A and C be x,

x + x + (x – 8) + 28 = 20 * 4

3x + 20 = 80

3x = 60

x = 20

The present age of C = 20 years

77. The age of A, 5 years ago and the age of B, 7 years hence is in the ratio of 5: 6. C is 7 years younger than D, who is 2 years elder than B. Find the present age of D, if the average present age of A, B, C and D is 24 years?

5 वर्ष पहले A की आयु और 7 वर्ष बाद B की आयु 5: 6 के अनुपात में है। C, D से 7 वर्ष छोटा है, जो B से 2 वर्ष बड़ा है| D की वर्तमान आयु ज्ञात कीजिए, यदि A, B, C और D की औसत वर्तमान आयु 24 वर्ष है?

A. 25 years
B. 30 years
C. 32 years
D. 27 years
E. None of these

Option “A” is correct.

The age of A, 5 years ago and the age of B, 7 years hence is in the ratio = 5: 6

Present age of A and B = 5x + 5, 6x – 7

D = B + 2 = 6x – 7 + 2 = 6x – 5

C = D – 7 = 6x – 5 – 7 = 6x – 12

The average present age of A, B, C and D = 24 years

5x + 5 + 6x – 7 + 6x – 5 + 6x – 12 = 24 * 4

23x – 19 = 96

23x = 115

x = 115/23 = 5

The present age of D = 6x – 5 = 25 years

78. Four times the difference in ages of Chetan and Anil is one more than the age of Binod. The ratio of the Anil’s age to Chetan’s age is 3:4. If ratio of Binod’s age 5 years hence to Chetan’s age 1 year ago is 4: 3. Find the average of ages Anil and Chetan.

चेतन और अनिल की आयु में अंतर का चार गुना, बिनोद की आयु से एक अधिक है। अनिल की आयु से चेतन की आयु का अनुपात 3:4 है| यदि 5 वर्ष बाद बिनोद की आयु से 1 वर्ष पहले चेतन की आयु का अनुपात 4:3 है। अनिल और चेतन की औसत आयु ज्ञात कीजिए।

A. 10
B. 14
C. 15
D. 25
E. None of these

Option “B” is correct.

4 (C-A) = B + 1 —- (1)

A/C * 100 = 75 => A/C = 75/100 = ¾

Sub from eqtn (1)

4 (4x-3x) = B+1

16x -12x =B+1

4x -1= B —- (2)

(B+5)/(C-1) = 4/3

(4x-1+5)/(4x-1) =4/3

(4x+4)/(4x-1) =4/3

12x +12 = 16x-4

4x =16=> x =4

=> A = 12, C = 16

=> Required average = 28/2 = 14

79. Ratio of the ages of Sania, Saina and Sindhu is 9: 6: 7 and the average ages of all of them after 12 years is 41 years and 4 month. If the ratio of the ages of Hima to Saina is 5: 6, then what is the average age of Saina, Sindhu and Hima?

सानिया, सायना और सिंधु की आयु का अनुपात 9: 6: 7 है और 12 साल के बाद उन सभी की औसत आयु 41 साल 4 महीने है। यदि हेमा और सायना की आयु का अनुपात 5: 6 है, तो सायना, सिंधु और हेमा की औसत आयु क्या है?

A. 22 years
B. 23 years
C. 24 years
D. 21 years
E. None of these

Option “C” is correct.

Sania + Saina + Sindhu = (41 + 4/12) * 3 – 36 = 88

Saina = 6/22 * 88 = 24 years

Hima = 5/6 * 24 = 20 years

Sindhu = 7/22 * 88 = 28

Required average = (24 + 20 + 28)/3 = 24 years

80. Ratio of the ages of Rahul to Bharathi is 4: 5 and the Kavin is 5 years elder than Bharathi. If the average age of Rahul, Bharathi and Kavin is 25 years, then what is the difference between the ages of Rahul and Kavin?

राहुल से भारती की आयु का अनुपात 4: 5 है और काविन, भारती से 5 वर्ष बड़ा है। यदि राहुल, भारती और काविन की औसत आयु 25 वर्ष है, तो राहुल और काविन की आयु के बीच में क्या अंतर है?

A. 5 years
B. 10 years
C. 15 years
D. 20 years
E. None of these

Option “B” is correct.

B = K – 5

R/B = 4/5

R = 4/5 * (K – 5)

4/5 * (K – 5) + K – 5 + K = 75

4K – 20 + 5K – 25 + 5K = 75 * 5

14K = 375 + 20 + 25

K = 30

R = 4/5 * (25) = 20

Difference = 30 – 20 = 10

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131 thoughts on “Problems on Ages”

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