The average age of a cricket team of 11 players is the same as it was 3 years back because 3 of the players whose current average age of 33 years are replaced by 3 youngsters. The average age of the new comers is :
(A) 23 years
(B) 21 years
(C) 22 years
(D) 20 years
Solution:
According to the question, Increased age of 11 players = 11 × 3 = 33 years Current age of 3 players who are replaced = 3 × 33 = 99 years ∴ Age of 3 newcomers = 99 - 33 = 66 years ∴ Average age = $$\frac{66}{3}$$ = 22 years
462.
The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:
(A) 3500
(B) 4000
(C) 4050
(D) 5000
Solution:
Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 x 2) = 10100 .... (i) Q + R = (6250 x 2) = 12500 .... (ii) P + R = (5200 x 2) = 10400 .... (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv) Subtracting (ii) from (iv), we get P = 4000 Therefore P's monthly income = Rs. 4000
463.
The average age of A, B, C, D and E is 40 years. The average age of A and B is 35 years and the average of C and D is 42 years. Age of E is :
(A) 48 years
(B) 46 years
(C) 42 years
(D) 45 years
Solution:
A + B + C + D + E = 40 × 5 = 200 A + B = 35 × 2 = 70 C + D = 42 × 2 = 84 Therefore, E = (A + B + C + D + E) - (A + B + C + D) E = 200 - 70 - 84 E = 46 years
464.
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 17 kg
(B) 20 kg
(C) 26 kg
(D) 31 kg
Solution:
Let A, B, C represent their respective weights. Then, we have : A + B + C = (45 × 3) = 135.....(i) A + B = (40 × 2) = 80.....(ii) B + C = (43 × 2) = 86.....(iii) Adding (ii) and (iii), we get: A + 2B + C = 166.....(iv) Subtracting (i) from (iv), we get: B = 31 ∴ B's weight = 31 kg
465.
A student finds the average of ten 2 digits numbers. While copying numbers, by mistake, he writes in number with its digits interchanged. As a result his answer is 1.8 less than the correct answer. The difference of digits of the number, in which he made mistake is ?
(A) 2
(B) 3
(C) 4
(D) 6
Solution:
Let us consider by mistake he writes 10th number with its digits interchanged. $$\therefore \frac{{10x + y - \left( {10y + x} \right)}}{{10}} = 18$$ (In this remaining nine numbers are same and they cancel out) ∴ 10x + y - 10y - x = 18 ⇒ 9x - 9y = 18 ⇒ x - y = 2
466.
Out of 20 boys, 6 are each of 1 m 15 cm height, 8 are of 1 m 10 cm and rest of 1 m 12 cm. The average height of all of them is :
(A) 1 m 12.1 cm
(B) 1 m 21.1 cm
(C) 1 m 21 cm
(D) 1 m 12 cm
Solution:
According to the question, Height of 6 persons= 6 × 1 m 15 cm = 6 m 90 cm Height of 8 persons= 8 × 1 m 10 cm = 8 m 80 cm Height of 6 persons= 6 × 1 m 12 cm = 6 m 72 cm Total Height of 20 persons= 22 m 42 cm Average = $$\frac{{22{\text{ m }}42{\text{ cm}}}}{{20}}$$ = 1 m 12.1 cm
467.
What is the difference between the average of first 148 even positive numbers and the average of first 129 odd positive numbers?
(A) 20
(B) 23
(C) 21
(D) 19
Solution:
Average of first 148 positive number $$\eqalign{ & = \frac{{N\left( {N + 1} \right)}}{N} \cr & = N + 1 \cr & = 148 + 1 \cr & = 149 \cr} $$ Average of first 129 odd number $$ = \frac{{{N^2}}}{N} = N = 129$$ Difference = 149 - 129 = 20
468.
A man bought 13 articles at Rs. 70 each, 15 at Rs. 60 each and 12 at Rs. 65 each. The average price per article is -
A, B, C and D are four consecutive even numbers respectively and their average is 65. What is the product of A and D?
(A) 3968
(B) 4092
(C) 4216
(D) 4352
Solution:
Let x, x + 2, x + 4 and x + 6 represent numbers A, B, C and D respectively. Then, $$\eqalign{ & \Rightarrow \frac{{x + \left( {x + 2} \right) + \left( {x + 4} \right) + \left( {x + 6} \right)}}{4} = 65 \cr & \Rightarrow 4x + 12 = 260 \cr & \Rightarrow 4x = 248 \cr & \Rightarrow x = 62 \cr} $$ So, A = 62, B = 64, C = 66, D = 68 ∴ A × D = 62 × 68 = 4216
470.
A school has 4 sections of chemistry in Class X having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.