1)Five years ago the average age of a family of 3 members was 27 years. A child has Been born, due to which the average age of the family is 25 years today. What is the Present age of the child?
Sol: Average age of the family of 3 members
5 years ago = 27 years
Sum of the ages of the 3 members now
= (27 + 5) * 3 = 96 years
Average age of the family of 4 members now
= 25 years
Sum of the ages of the 4 numbers now
= 25*4 = 100 years
Age of child = 100 – 96 = 4 years
2) In a class of 20 students in an examination in Mathematics 2 students scored 100 Marks each, 3 get zero each and the average of the rest was 40. What is the average of the whole class?
Sol: Total marks obtained by a class of 20 students
= 2 * 100 + 3 * 0 + 15 * 40
= 200 + 600 = 800
: Average marks of whole class = 800/20 = 40
3).The greatest number, which can divide 432, 534 and 398 leaving the same remainder 7 in each, is
Required number is the H.C.F of
(432-7), (534-7) and (398-7)
i.e., H.C.F. of 425, 527, 391
Required number = 17
4) The sum of two numbers is 216 and their H.C.F is 27. The numbers are
Let the numbers be 27a and 27b
Then 27a + 27b = 216
a+b = 8
Value of co-primes a and b are (1,7) (3,5)
: . Numbers are (27*1, 27*7) = (27,189)
5) The greatest number of 4 digits which is divisible by each one of the number 12,18, 21 and 28 is
Greatest number of 4 digits is 9999
L.C.M of 12, 18, 21, 28 = 252
On dividing 9999 by 252, the remainder is 171
: . Required number is (9999-171) = 9828
6) Four prime numbers are arranged in ascending order according to their magnitude Product of first three is 385 and the product of last three is 1001. The greatest number is.
1) 11
2) 13
3) 17
4) 19
Sol: 2) 385) 1001(2
770
231) 385(1
231 (1
154)231(1
154
77) 154(2
154
0
Hence the product of the middle terms = 77
Greatest prime number = 1001 / 77 = 13.
7) If the square root of 55625 is 75, then
√5625 + √56.25 + √0.5625 is equal to
1) 82.25
2) 83.25
3) 80.25
4) 79.25
____ _____ ______
Sol: 2) √5625 = 75; √56.25 = 7.5; √. 5625 = .75
-- > 75+7.5+0.75 = 83.25
8) Which of the following integers has most number of divisors?
1) 176
2) 182
3) 99
4) 101
Sol: 2) 176 = 2,4,8,11,16,22,44,88
182 = 2,7,13,14,26,91
99 = 3, 9, 11, 33
101= 101
9) A boy was asked to find the value of 3/8 of a sum of money. Instead of multiplying the sum by 3/8 he divided it by 3/8 and then his answer exceeded by Rs. 55. Find the Correct be x?
Sol: Let amount be x
8/3* - 3/8 * = 55
-- > 64x – 9x/24 = 55 -- > 55x/24 = 55
-- > x = 24*55/55 = 24
: . 3/8 of x = 3/8 * 24 = Rs.9
10) A boy was asked to find the value of 7/12 of a sum of money. Instead of multiplying The sum by 7/12 he divided it by 7/12 and thus his answer exceeded the correct Answer By Rs.95. Find the correct?
Sol: Let sum = Rs. K
: . 12/7 k – 7k/12 = 95
-- > 144k – 49k/84 = 95 -- > k = 84
:. 7/12 k -- > 7/12 * 84 = Rs. 49
11) In a boat 25 persons were sitting. Their average weight increased one kilogram when one man goes and a new man comes in. The weight of the new man is 70kgs. Find the Weight of the man who is going?
Sol: Weight increased per person is 1 kg.
Total increase in weight = 25 kgs
Weight of new man is 70 kgs,
(Which means his weight is 25 kgs heavier)
The weight of the old man was 70 – 25 = 45 kgs
13) What is the greatest possible length that can be used to measure exactly the following Lengths 7m, 3m 85cm, and 12m 95cm?
The length to be measured is700cm, 385cm, 1295cm.
The required length in cm is the H.C.F of 700, 385, and 1295, which is 35 cm.
14) The product of two-digit number is 2160 and their H.C.F is 12. The numbers are
Let the number are 12a and 12b
Then 12a * 12b = 2160
ab = 15
Value of co-primes a and b are (1, 15) (3,5)
: . The two digit numbers are (3*12, 5*12)
= (36, 60)
15) The least number of 6 digits which it exactly divisible by 12, 15 and 18 is
Least number of 6 digits is 100000
L.C.M of 12, 15, 18, is 180.
On dividing 100000 by 180, the remainder is 100
. Required number = 100000 + (180-100) = 100080
16) Two third of three fifth of one fourth of a number is 24. What is 40% of that number?
1) 96
2) 72
3) 120
4) 156
Sol: 1) let the number be x, then
X of 2/3 of 3/5 of ¼ = 24
X * 2/3 * 3/5 * ¼ = 24, x = 240.
Hence 40% of 240 = 40/100 * 240 = 96
Submitted by Subbaiah
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