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- Question
In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options- A. 159
- B. 194
- C. 205
- D. 209
- E. None of these
- Correct Answer
- 209
ExplanationWe may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).∴ Required number
of ways= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4) = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2) = (6 x 4) + ❨ 6 x 5 x 4 x 3 ❩ + ❨ 6 x 5 x 4 x 4 ❩ + ❨ 6 x 5 ❩ 2 x 1 2 x 1 3 x 2 x 1 2 x 1 = (24 + 90 + 80 + 15) = 209.
More questions
- 1. The age of a father 10 years ago was thrice the age his son. Ten years later, the father's age will be twice that of his son. The ratio of their present ages is?
Options- A. 8 : 5
- B. 7 : 3
- C. 5 : 2
- D. 9 : 5 Discuss
Correct Answer: 7 : 3
Explanation:
Let son's age 10 years ago be x years.
? father's age 10 years ago = 3x years
? 3x + 20 = 2(x + 20)
? x = 20
? Ratio of their present ages = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3- 2. The ratio of Laxmi's age of the age of her mother is 3 : 11. the difference of their ages is 24 years. The ratio of their ages after 3 yeras will be?
Options- A. 1 : 3
- B. 2 : 3
- C. 3 :5
- D. None of these Discuss
Correct Answer: 1 : 3
Explanation:
Let the ages of Laxmi and her mother be 11x and 3x respectively.
From question, 11x - 3x = 24
? x = 3
? Ratio of their ages after 3 years = ( 3x + 3) : (11x + 3 )
= 12: 36 = 1 : 3- 3. The total ages of A, B and C at present is 90 years. Ten years ago the ratio of their ages was 1 : 2 : 3. Then the present age of B is ....?
Options- A. 30 years
- B. 20 years
- C. 40 years
- D. None of these Discuss
Correct Answer: 30 years
Explanation:
Let the respective ages of A, B and C, ten years ago be x, 2x and 3x years.
? (x + 10) + (2x + 10) + ( 3x + 10) = 90
? 6x = 60
? x = 10
? B's present age = 2x + 10 = 30 years- 4. A father's age is four times as much as the sum of the ages of his three children but 6 years hence his age will be only double the sum of their ages. Then the age of the father is?
Options- A. 30 years
- B. 40 years
- C. 60 years
- D. 45 years Discuss
Correct Answer: 60 years
Explanation:
Let father's age be x years and the sum of ages of children be y years.
? x = 4 y ....(i)
Also (x + 6) = 2(y + 6 + 6 + 6) ....(ii) [6 is added thrice for three children ]
Solving (i) and (ii)
x = 60 years, and y = 15 years.- 5. Present age of Rahul is 8 years less then Ritu's present age. If three years ago Ritu's age was x, which of the following represents Rahul's present age?
Options- A. x + 3
- B. x - 5
- C. x - 3 + 8
- D. x + 3 + 8 Discuss
Correct Answer: x - 5
Explanation:
Let the Rahul's present age is 'A' years. Then Ritu's present age is (A + 8)
Now, according to the question,
(A + 8) - 3 = x
? A = (x - 5) years- 6. The ratio in the ages of A and B, 1 year ago was 3 : 4. While it will be 5 : 6 after 1 year. What is the present age of B?
Options- A. 8 years
- B. 4 years
- C. 6 years
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Let the present age of A and B be x and y years respectively
From 1st condition
(x - 1) / (y -1) = 3/4
? 4x - 4 = 3y - 3
? 4x - 3y = 1 ... (i)
From 2nd condition,
(x + 1) / (y + 1) = 5/6
? 6x + 6 = 5y + 5
? 6x - 5y = -1 ...(ii)
Multiplying equation (i) by 3 and equation (ii) by 2 and subtract
y = 5
? Present age of B = 5 years- 7. If A son is younger then his father by 25 years and the father was 45 years old,4 years ago. What will be the total age of the father and son after 5 years?
Options- A. 82 years
- B. 88 years
- C. 83 years
- D. 78 years Discuss
Correct Answer: 83 years
Explanation:
Let the present age of father be x years, Then the present age of son = (x - 25) years .
According to to question,
x - 4 = 45
? x = 45 + 4
? x = 49
? Age of son = 49 - 25 = 24 years
? Age of son after five years = 24 + 5 = 29 years
? Age of father after five years = 49 + 5= 54 years
Total age of both = 29 + 54= 83 years- 8. The ratio of the ages of Ram and Rahim 10 yr ago was 1 : 3 . The ratio of their ages five years hence will be 2 : 3. Then, the ratio of their present ages is?
Options- A. 1 : 2
- B. 3 : 5
- C. 3 : 4
- D. 2 : 5 Discuss
Correct Answer: 3 : 5
Explanation:
Let 10 yr ago, ages of Ram and Rahim were k yr and 3k yr, respectively.
Then, present age of Ram = (k + 10)
and present age of Rahim = (3k + 10)
According to the question, (k + 10 + 5) / (3k + 10 + 5) = 2/3
? 3k + 45 = 6k + 30
? 3k = 15
? k = 5
Hence, required ratio = (5 + 10) / (3 x 5 + 10)
= 15/25
= 3 : 5- 9. The present age of Ravi's father is four times Ravi's present age.Five years back, Ravi's father was seven times as old as Ravi was at that time. What is the present age of Ravi's father?
Options- A. 84 yr
- B. 70 yr
- C. 40 yr
- D. 35 yr Discuss
Correct Answer: 40 yr
Explanation:
Let present age of Ravi be k.
Then, Present age of Ravi's father = 4k.
Now, 5 yr ago,
Ravi's father's age = 7 x Ravi's age
? 4k - 5 = 7(k - 5)
? 4k - 5 = 7k - 35
? 3k = 30
? k = 10
? Ravi's present age = k = 10 yr
? Ravi's father's present age = 4k
= 4 x 10 = 40 yr- 10. If the two digits of the age of Mr. Manoj are reversed then the new age so obtained is the age of his wife. 1/11 of the sum of their ages is equal to the difference between their ages. If Mr. Manoj is elder than his wife then find the difference their ages?
Options- A. Cannot be determined
- B. 10 years
- C. 8 years
- D. 9 years Discuss
Correct Answer: 8 years
Explanation:
Let the age of Mr Manoj be (10y + y) yrs.
? His wife's age = (10y + x ) years
Then, ((10x + y + 10y + x) / 11 = 10x + y -10y-x
? x + y = 9x - 9y
? 8x = 10y
? x/y = 5/4
? x = 5 and y =4 (because any other multiple of 5 will make x of two digits).
? Diff. = (10x + y) - (10y - x)
= 9x - 9y
= 9(x-y)
= 9(5-4)
= 9 yrs.
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