年齡問題 - 例題解析

題1 - 如果兩個人 राम 和 sham 的年齡比例是 5:4。三年後，他們的年齡比例變為 11:9。在這種情況下，請說明 sham 先生現在的年齡。

答案 - B

解釋

If the age of Mr. Ram  5x and 4x is the age of Mr. sham.
Then, ( 5x+3) /( 4x+3) = 11/9  ⇒ 9 (5x+3)= 11 (4x+3) ⇒ x= (33-27) = 6
So the present age of Mr. sham = 6*4 = 24 years.

題2 - 一個母親比她的女兒大 30 倍。18 年後，母親的年齡將是女兒的三倍。在這種情況下，請說明母親現在的年齡。

答案 - A

解釋

Let  daughter present age   be  x year .
in that case mother  present age would be = 30x years  
30x+ 18 = 3 (x+ 18) ⇒ 27x = 36  ⇒ x = 4/3  
∴ so the present age of mother = (30* 4/3) = 40 years.

題3 - 三個人 ajay、vijay 和 sanjay 現在的年齡比例為 4:7:9。8年前，他們年齡的總和是 56。他們的現在年齡是多少？

答案 - A

解釋

If the present age of ajay , vijay and sanjay is  4x , 7x and 9x years.
Total sum of  ages of ajay, vijay and sanjay  before 8 years  ago = (4x-8)+(7x-8)+(9x-8)
=(20x-24) years.
∴ 20x-24 = 56 ⇒ 20x = 80 ⇒ x= 4 
Hence,  it proves that age of ajay is 4*4 = 16 years, 
vijay (7*4) = 28 years  and sanjay  (9* 4) = 36 years.

題4 - 女兒的現在年齡是她母親的 2/5。8 年後，女兒的年齡將是她母親年齡的 1/2。求母親現在的年齡？

答案 - B

解釋

If the present age of mother is  equal to  x year.  
In that situation the daughter present age would be = 2x/5 years.
2x/5 + 8 = 1/2 (x+8) ⇒  4x+ 80 = 5x+40 ⇒ x = 40.
The mother age at the present time is = 40 years.

題5 - 3年前，Ajay 的年齡是 Bhuvan 的兩倍。七年後，兩人的年齡之和將是 83 歲。他們現在的年齡是多少？

答案 - C

解釋

Before  3 year  let  bhuvan age be x years. 
3 years before , ajay age will be  2x years. 
Now Bhuwan's  age =(x+3) years and ajay  age = (2x+3) years.
(x+3)+7+(2x+3)+7 = 83 ⇒  3x+20 = 83 ⇒ 3x = 63 ⇒ x = 21 
Now the bhuwan present age = (21+3) = 24 years 
Now the ajay present age = (2 *21+3) years = 45 years.

題6 - 我比我姐姐大 4 歲，但我弟弟是我們中最小的，比我小 7 歲。我父親的年齡是我的弟弟的三倍。我姐姐現在的年齡是 18 歲，我父親比我母親大 3 歲。在這種情況下，我母親現在的年齡是多少？

答案 - A

解釋

If my sister age is x years. Then,
Sister  -    x 
I   -       x+4
Brother -  (x+4-7) = x-3
Father - 3 (x-3) 
Given x = 18
∴  Father's age =  3(18-3) = 45 years.
Mother age = (45-3) = 42 years.

題7 - Ajay 比 Vijay 小的年齡與他比 Vinay 大的年齡相同。如果 Vijay 和 Buwan 的年齡之和為 48 歲，那麼 Ajay 先生現在的年齡是多少？

答案 - D

解釋

V-A = A- B ⇒ V+B = 2A =48 ⇒ 24
Now,  We can say that the present age  of Mr. Ajay  is 24 years.

題8 - 如果父親和兒子的年齡之和為 100 歲。5年前，父親和兒子的年齡比例為 2:1。求出10年後的年齡比例。

答案 - D

解釋

If the age of father at the present time = x years 
His son age at the present time =  (100-x) years.
x-5 / (100-x-5) = 2/1  ⇒ (x-5) = 2(95-x) ⇒ 3x = 195  ⇒ x = 65
Ratio of the ages of man and son after 10 years = (65+10)/(35+10)= 75/45 = 5/3 = 5:3

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