Present average of age of A and B is 6x – 15 years. Present average age of A, B and C is 4x + 6 years. If present age of B is 25% less than the present age of C and 20% more than the present age of A, then find the present age of A.
Sum of the present age of A and B = 2 × (6x – 15) = 12x – 30 years
Sum of the present age of A, B and C = 3 × (4x + 6) = 12x + 18 years
So, the present age of C = 12x + 18 – 12x + 30 = 48 years
Present age of B = 48 × 0.75 = 36 years
Present age of A =
36
= 30 years
1.2
Hence, option A is correct.
1
A और B की वर्तमान आयु का औसत 6x - 15 वर्ष है। A, B और C की वर्तमान औसत आयु 4x + 6 वर्ष है। यदि B की वर्तमान आयु C की वर्तमान आयु से 25% कम है और A की वर्तमान आयु से 20% अधिक है, तो A की वर्तमान आयु ज्ञात कीजिए।
Sum of the present age of A and B = 2 × (6x – 15) = 12x – 30 years
Sum of the present age of A, B and C = 3 × (4x + 6) = 12x + 18 years
So, the present age of C = 12x + 18 – 12x + 30 = 48 years
Present age of B = 48 × 0.75 = 36 years
Present age of A =
36
= 30 years
1.2
Hence, option A is correct.
A
2
The age of Arjun is (x + 5) years. The ratio of the age of Arjun 2 years hence to the age of Draupadi 1 year before is 6 : 5 respectively. If Arjun is 4 years older than Draupadi, then find the age of Shubhadra whose age is 4 years less than the average age of Arjun and Draupadi taken together.
Since Arjun is 4 years older than Draupadi , so Age of Draupadi = (x + 1)
According to question,
(x + 5) + 2
=
6
(x + 1) – 1
5
5x + 35 = 6x
x = 35
So, age of Arjun and Draupadi is (35 + 5) = 40 years and (35 + 1) = 36 years respectively
Average age of Arjun and Draupadi =
40 + 36
= 38 years
2
Therefore, age of Shubhadra = (38 – 4) = 34 years
Hence, option C is correct.
2
अर्जुन की आयु (x + 5) वर्ष है। अर्जुन की 2 वर्ष बाद की आयु द्रौपदी की 1 वर्ष से पहले की आयु का अनुपात क्रमशः 6: 5 है। यदि अर्जुन द्रौपदी से 4 वर्ष बड़ा है, तो शुभद्रा की आयु ज्ञात करें, जिसकी आयु अर्जुन और द्रौपदी की औसत आयु से 4 वर्ष कम है।
Since Arjun is 4 years older than Draupadi , so Age of Draupadi = (x + 1)
According to question,
(x + 5) + 2
=
6
(x + 1) – 1
5
5x + 35 = 6x
x = 35
So, age of Arjun and Draupadi is (35 + 5) = 40 years and (35 + 1) = 36 years respectively
Average age of Arjun and Draupadi =
40 + 36
= 38 years
2
Therefore, age of Shubhadra = (38 – 4) = 34 years
Hence, option C is correct.
C
3
Arun and Meena recently celebrated their golden anniversary and their daughter Seema’s birthday. If the age of Seema 18 years after her parents’ marriage and her age at their golden anniversary is in the ratio 5 : 21, how many years after the marriage was Seema born?
Let the age of seema at their silver anniversary = K yrs
18 yrs of marriage = 7 yrs before silver anniversary
Age of seema 7yrs before silver anniversary = K – 7
Seema’S age 25 yrs after silver anniversary (golden anniversary) = K + 25
K – 7
=
5
K + 25
21
K = 17yrs
Seema’s age on silver anniversary = 17yrs
She is born 25 – 17 yrs = 8yrs after the marriage.
Hence, option A is correct.
Alternate Solution:-
Let the age of Seema 18 years after her parents marriage be 5k years
So age of Seema at golden anniversary of her parents = (5k + 32) years
From the question,
5k / (5k + 32) = 5 / 21
or, k =2
So Seema's age was 10 , when her parents had completed 18 years of marriage.
So Seema was born 8 years after her parents marriage.
Hence, option A is correct.
3
अरुण और मीना ने हाल ही में अपनी स्वर्ण वर्षगांठ और अपनी बेटी सीमा का जन्मदिन मनाया। यदि माता-पिता के विवाह के 18 वर्ष बाद सीमा की आयु और उनकी स्वर्ण वर्षगांठ पर उसकी आयु 5: 21 के अनुपात में है, तो विवाह के कितने वर्ष बाद सीमा का जन्म हुआ था?
Let the age of seema at their silver anniversary = K yrs
18 yrs of marriage = 7 yrs before silver anniversary
Age of seema 7yrs before silver anniversary = K – 7
Seema’S age 25 yrs after silver anniversary (golden anniversary) = K + 25
K – 7
=
5
K + 25
21
K = 17yrs
Seema’s age on silver anniversary = 17yrs
She is born 25 – 17 yrs = 8yrs after the marriage.
Hence, option A is correct.
Alternate Solution:-
Let the age of Seema 18 years after her parents marriage be 5k years
So age of Seema at golden anniversary of her parents = (5k + 32) years
From the question,
5k / (5k + 32) = 5 / 21
or, k =2
So Seema's age was 10 , when her parents had completed 18 years of marriage.
So Seema was born 8 years after her parents marriage.
Hence, option A is correct.
A
4
Seven years later from now A will be as old as B was 4 years ago. C was born 2 years ago. The average age of A, B and C 10 years later will be 33yrs. What is the present age of A?
Let age of A 7 years later be k so age of B 4 years ago was k
C was born 2 years ago so age of C 10 yrs later will be 12 years
4 years ago
Present
7 years later
10 years later
A
k – 11
k – 7
k
K + 3
B
k
K + 4
K + 11
K + 14
C
2
9
12
Average age of all three 10 yrs later = 33
K + 3 + k + 14 + 12
= 33
3
2k + 29 = 99 → 2k = 70 → k = 35
Present age of A = k – 7 = 35 – 7 = 28 years
Hence, option B is correct.
4
अब से सात साल बाद A उतना ही बड़ा होगा जितना B 4 साल पहले था। C का जन्म 2 साल पहले हुआ था। A, B और C की औसत आयु 10 वर्ष बाद 33 वर्ष होगी। A की वर्तमान आयु क्या है?
Let age of A 7 years later be k so age of B 4 years ago was k
C was born 2 years ago so age of C 10 yrs later will be 12 years
4 years ago
Present
7 years later
10 years later
A
k – 11
k – 7
k
K + 3
B
k
K + 4
K + 11
K + 14
C
2
9
12
Average age of all three 10 yrs later = 33
K + 3 + k + 14 + 12
= 33
3
2k + 29 = 99 → 2k = 70 → k = 35
Present age of A = k – 7 = 35 – 7 = 28 years
Hence, option B is correct.
B
5
P’s age 8 years ago is equal to the sum of the present ages of his son and his daughter. 5 years hence, the ratio between his daughter’s age and his son’s age will be 7 : 6 respectively. P’s wife is 7 years elder than him. His wife’s present age is thrice the present age of his son. What is his daughter’s present age?
Let 5 years hence the age of daughter and son be 7x years and 6x years respectively, then
Present age of daughter= (7x – 5) years
Present age of son = (6x – 5)years
⇒ Present age of P = [(7x – 5) + (6x – 5) + 8] = (13x – 2)years
∴ Present age of P's wife = [(13x – 2) + 7] = (13x + 5) years
Given, present age of P's wife is thrice the present age of his son.
(13x + 5) = 3(6x – 5)
⇒ x = 4
Hence, his daughter’s present age = (7x – 5) = 23 years.
Hence, option C is correct.
5
P की आयु 8 वर्ष पहले उसके पुत्र और उसकी पुत्री की वर्तमान आयु के योग के बराबर है। 5 साल बाद, उनकी बेटी की उम्र और उनके बेटे की उम्र के बीच का अनुपात क्रमशः 7: 6 होगा। P की पत्नी उनसे 7 साल बड़ी है। उनकी पत्नी की वर्तमान आयु उनके पुत्र की वर्तमान आयु की तीन गुनी है। उनकी बेटी की वर्तमान आयु क्या है?
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