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- Question
- The average age of two boys and their father is greater then average age of those two boys and their mother by 3 yr. The average age of the four is 19 yr. If the average age of the two boys be 5 1/ 2, then find the age of the father and mother.
Options- A. 37 yr and 28 yr
- B. 47 yr and 38 yr
- C. 50 yr and 41 yr
- D. 35 yr and 32 yr
- Correct Answer
- 37 yr and 28 yr
ExplanationLet the ages of mother, father and boys be M, F, B1 and B2, respectively.
The total age of four member
= 19 x 4
= 76 yr.
Given (B1 + B1)/2 = 11/2
? B1 + B2 = 11
M + F + B1 + B2 = 76 - 11
? M + F = 65 .......(i)
According to the question,
(B1 + B2 + F) / 3 = (B1 + B2 + M) / 3 + 3
? B1 + B2 + F) = B1 + B2 + M + 9
? F = M + 9
? F - M = 9 ............. (ii)
From Eqs (i) and (ii), we get
F = 37 yr and M = 28 yr - 1. A rectangle has 20 cm as its length and 200 sq cm as its area. If the area is increased by 1 1/ 5 time the original area by increase its length only then the perimeter of the rectangle so formed (in cm) is
Options- A. 72
- B. 60
- C. 64
- D. 68 Discuss
- 2. The perimeter of an isosceles triangle is 26 cm while equal sides together measure 20 cm. The third side and each of the equal sides are respectively.
Options- A. 6 cm and 10 cm
- B. 8 cm and 9 cm
- C. 10 cm and 8 cm
- D. 14 cm and 6 cm Discuss
- 3. If the diagonals of a rhombus are 4.8 cm 1.4 cm, then what is the perimeter of the rhombus?
Options- A. 5 cm
- B. 10 cm
- C. 12 cm
- D. 20 cm Discuss
- 4. The average of first nine multiples of 3 is?
Options- A. 12.0
- B. 12.5
- C. 15.0
- D. 18.5 Discuss
- 5. A number 15 is divided into 3 parts which are in Arithmetic Progression (A.P) and the sum of their squares is 83. What will be the smallest number?
Options- A. 5
- B. 3
- C. 6
- D. 8 Discuss
- 6. Find the number of combinations that can be formed with 5 oranges, 4 mangoes and 3 bananas, when one fruit of each kind is taken.
Options- A. 60
- B. 120
- C. 110
- D. 75 Discuss
- 7. The diagonals of two squares are in the ratio of 3 : 2. Find the ratio of their areas.
Options- A. 9 : 4
- B. 9 : 2
- C. 9 : 5
- D. 9 : 7 Discuss
- 8. The diagonals of a squares is 4?2 cm. The diagonal of another square whose area is double that of the first square is
Options- A. 8 cm
- B. 8?2 cm
- C. 4?2 cm
- D. 6 cm Discuss
- 9. The lengths of three line segments (in cm) are given in each of the four cases. Which one of the following cases is not suitable to be the three sides of a triangle?
Options- A. 2, 3, 4
- B. 2, 3, 5
- C. 2, 4, 5
- D. 3, 4, 5 Discuss
- 10.
If a = ? 3 - ? 2 , b = ? 3 + ? 2 , then the value of ?3 + ?2 ?3 - ?2 a 2 + b 2 is : b a
Options- A. 900
- B. 970
- C. 1030
- D. 930 Discuss
More questions
Correct Answer: 68
Explanation:
l1 = 20 cm, A1 = 200 sq cm
? b1 = 200/20 = 10 cm
Now, A2 = 200 x 6/5 = 240 sq cm
b2 = 10 cm
? l2 = 240/10 = 24 cm
? Perimeter of new rectangle = 2(l2 + b2)
= 2(24 + 10) = 2 x 34 = 68 cm
Correct Answer: 6 cm and 10 cm
Explanation:
Let the third side be x.
According to the question,
x + 20 = 26
? x = 26 - 20 = 6 cm
? Each equal side = 20/2 = 10 cm
Correct Answer: 10 cm
Explanation:
Perimeter of rhombus
= 2 ? d1 2 + d2 2
= 2 ?(4.8)2 + (1.4)2
= 2 ?23.04 + 1.96
= 2 ?25
= 2 x 5 = 10 cm
Correct Answer: 15.0
Explanation:
Average = ( 3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 ) / 9
= 3(1+2+3+4+5+6+7+8+9)/9
= ( 45 / 3 )
= 15
Correct Answer: 3
Explanation:
Let us assume the second number is a and the difference between consecutive numbers is d.
According to Arithmetic progression,
First number = a - d
Second number = a
Third number = a + d
According to question,
Sum of the all three numbers = 15
a - d + a + a + d = 15
3a = 15
a = 5
Again according to given question,
sum of square of the 3 numbers = 83
(a - d) 2 + a 2 + (a + d) 2 = 83
apply the algebra formula
a 2 + d 2 - 2ad + a 2 + a 2 + d 2 + 2ad = 83
3a 2 + 2d 2 = 83
Put the value of a in above equation.
3 x 5 2 + 2d2 = 83
3 x 25 + 2d2 = 83
75 + 2d2 = 83
2d 2 = 83 - 75
2d 2 = 8
d 2 = 8/2
d 2 = 4
d = 2
Put the value of a and d in below equation.
First number = a - d = 5 - 2 = 3
Second number = a = 5
Third number = a + d = 5 + 2 = 7
The smallest number is 3.
Correct Answer: 60
Explanation:
The required number of combinations, when one fruit of each kind is taken
= 5C1 x 4C1 x 3C1 = 5 x 4 x 3 = 60
Correct Answer: 9 : 4
Explanation:
Let the diagonals of the squares be 3x and 2x.
? Ratio of their areas = [(1/2) (3x2)] / [(1/2) (2x2)] = 9/4
Correct Answer: 8 cm
Explanation:
Diagonal of square = ?2a [a = side]
4?2 = ?2 a
a = 4 cm
Now, area of square = a2 = (42) = 16
Side of a square whose area is 2 x 16.
a12 = 32
? a1 = ?32 ?a14?2
Now, diagonal of new square = ?2a
= ?2x 4 ?2
= 8 cm
Correct Answer: 2, 3, 5
Explanation:
We know that in any triangle
"the sum of two sides is always greater than its third side" and
"the difference of two sides is always less than its third side".
(i) 2 + 3 is not greater than 5
(ii) |5 - 2| not less than 3
Correct Answer: 970
Explanation:
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