1) The average ages of three persons is 27 years. Their ages are in the proportion of 1:3:5.What is the age in years of the youngest one among them?
Sol: Let the age of three persons be x, 3x and 5x
-- > 9x/3 = 27 -- > x = 9
2) The average of 11 numbers is 50. If the average of first 6 numbers is 49 and that of last 6 is 52.Find the 6th number?
Sol: The total sum of 11 results = 11 * 50 = 550
The total sum of first 6 results = 6 * 49 = 294
The total sum of last 6 results = 6 * 52 = 312
Sixth result = 294 + 312 – 550 = 56
3) Find L.C.M of 852 and 1491?
Sol: 852) 1491 (1
852
639) 852 (1
639
213) 639 (3
639
0
H.C.F of 852 and 1491 is 213
: . L.C.M = 852*1491/213 = 5964
4) The smallest number which when divided by 20, 25, 35, 40 leaves the remainder 6 When divided by 14, 19, 23 and 34 respectively is the difference between divisor and The corresponding remainder is 6?
: . Required number = (L.C.M of 20, 25, 35, 40) – 6
= 1400-6 = 1394
5) The least multiple of 7 which leaves a remainder 4 when divided by 6,9,15 and 18 is?
L.C.M of 6,9,15 and 18 is 90.
Let x be the least multiple of 7, which when divided by 90 leaves the remainder 4.
Then x is of the form 90k + 4.
Now, minimum value of k for which 90k + 4 is divisible by 4.
: . x = 4 * 90 + 4 = 364
6) Sum of three even consecutive numbers is 48, and then least number is?
1) 16
2) 18
3) 20
4) 14
Sol: 4) Let the numbers be 2n, 2n+2 and 2n+4
2n + (2n+2) + (2n+4) = 48
6n = 48-6 = 42, n = 7
Hence the numbers are -- > 14, 16 and 18
The least number is 14.
7) It being given that √ 15 = 3.88, the best approximation to √5/3 is
1) 0.43
2) 1.89
3) 1.29
4) 1.63
__ ___ __ __ __
Sol: 3) x = √5/3 = √5*3/3*3 = √15 /√ 9 = √15/3 = 3.88/3 = 1.29
8) Of the two-digit numbers (those from 11 to 95, both inclusive) how many have a Second digit greater than the first digit?
1) 37
2) 38
3) 36
4) 35
Sol: 3) 12 to 19 -- > 8
23 to 29 -- > 7
34 to 39 -- > 6
45 to 49 -- > 5
56 to 59 -- > 4
67 to 69 -- > 3
78 to 79 -- > 2
89 -- > 1
9) The Value of √24 + 3√64 + 4√28 is
Sol: 24*1/2 + 43*1/3 + 28*1/4
-- > 4 + 4 + 4 -- > 12
10) 3 ¼ - 4/5 of 5/6 / 4 1/3 / 1/5 – (3/10 + 21 1/5 ) is equal to
Sol: 13/4 – 4/5 * 5/6 / 13/3 / 1/5 – ( 3/10 + 106/5 ) (use BODMASRULE)
-- > 13/4 – 4/6 / 13/3 / 1/5 – 215/10 -- > 31/12 / 13/3 * 5 – 215/1
-- > 31/12 / 65/3 – 43/2 -- > 31/12 / 130 – 129/6 -- > 31/12/1/6 = 31/12 * 6/1
-- > 31/2 = 15 ½
11) 13 sheep’s and 9 pigs were bought for Rs. 1291.85.If the average price of a sheep be Rs. 74.What is the average price of a pig?
Sol: Average price of a sheep = Rs. 74
: . Total price of 13 sheeps
= (74*13) = Rs. 962
But, total price of 13 sheeps and 9 pigs
= Rs. 1291.85
Total price of 9 pigs
= Rs. (1291.85-962) = Rs. 329.85
Hence, average price of a pig
= (329.85/9) = Rs. 36.65
12) A batsman in his 18th innings makes a score of 150 runs and thereby increasing his Average by 6.Find his average after 18th innings?
Sol: Let the average for 17 innings is x runs
Total runs in 17 innings = 17x
Total runs in 18 innings = 17x + 150
Average of 18 innings = 17x + 150/18
: . 17x + 150/18 = x + 6 -- > x = 42
Thus, average after 18 innings = 42
13) Find the H.C.F of 777 and 1147.
777) 1147 (1
777
370) 777 (2
740
37) 370 (10
370
0
: . H.C.F of 777 and 1147 is 37.
14) The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 210 the other is?
The other number
= L.C.M * H.C.F/given number
= 2310*30/210 = 330
15) The average of 50 numbers is 38. If two numbers namely 45 and 55 are discarded, The average of remaining numbers is?
Total of 50 numbers = 50 * 38 = 1900
Average of 48 numbers = 1900-(45+55) / 48
= 1800 / 48 = 37.5
16) Divide 50 in two parts so that the sum of reciprocals is (1/12), the numbers are
1) 20,30
2) 24,36
3) 28,22
4) 36,14
Sol: 1) Let the numbers be x and y then
X+y = 50. ………(i)
1/x + 1/y = 12
1/x + 1/50-x = 1/12..From (i) y = 50 – x
-- > 50-x+x/x(50-x) = 1/12
-- > x2-50x+600 = 0
-- > (x-30) (x-20) = 0
submitted by subbaiah
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