General Mathematics

Question: Which of the following fractions is the smallest?
A
`13/16`

B
`15/19`

C
`17/21`

D
`7/8`

Note: We have: `13/16=0.8125,15/19=0.7894,17/21=0.8095` & `7/8=0.875.` The smallest of these is `15/19.'
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Question: 0.000006723 when expressed in scientific notation, is:
A
`6723 xx 10^-5`

B
`67.23 xx 10^-7`

C
`6.723 xx 10^-6`

D
None

Note: `0.000006723=0.000006723 xx 10^6/10^6 = 6.723/10^6=6.723 xx 10^-6.`
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Question: What decimal of an hour is a second?
A
.0025

B
.0256

C
.00027

D
.000126

Note: Required decimal=`1/60 xx 60 = 1/3600 = .00027`.
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Question: If `1.125 xx 10^k = 0.001125`, then the value of k is:
A
-4

B
-3

C
-2

D
-1

Note: `10^k = 0.001125/1.125 = 1.125/1125 = 1.125 xx 10^3/1125 xx 10^3 = 1/10^3 = 10^-3`. :. k=-3.
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Question: A and B can together finish a work in 30 days. They worked at it for 20 days and then B left. the remaining work was done by A alone in 20 more days. A alone can finish the work in :
A
48 days

B
50 days

C
54 days

D
60 days

Note: solution: Work done by A and B in 20 days = `(1/30 xx 20)` =`2/3`. Remaining work =`(1 - 2/3)` =`1/3`. Now, `1/3` work is done by A in 2o days `:.` Whole work will be done by A in `(20 xx 3) = 60` days.
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Question: A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but a leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was :
A
6

B
8

C
9

D
12

Note: solution: `(A + B)`'s 1 day's work = `(1/45 + 1/40)` =`17/360`. Work done by B in 23 days = `(1/40 xx 23)` =`23/40`. Remaining work = `(1 - 23/40)` =`17/40`. Now, `17/360` work was done by `(A + B)` in `(1 xx 360/17 xx 17/40)` = 9 days. `:.`A left after 9 days.
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Question: A dose half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it ?
A
30 days

B
35 days

C
40 days

D
none of these

Note: solution: Suppose B takes `X` days to do the work. `:.` A takes `(2 xx 3/4 x)` = `(3x)/2` days to do it. `(A + B)`'s 1 day's work = `1/18`. `:. 1/x + 2/(3x) = 1/18` or `x = 30`.
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Question: A can do a certain job in 12 days. B is 60% more efficient than A. The number of days, it take B to do the same piece of work, is :
A
6

B
`6 1/4`

C
`7 1/2`

D
8

Note: solution: Ration of times taken by A and B =`160 : 100 = 8 : 5`. `8 : 5 :: 12 : X` or `8x = 5 xx 12` or `x = 7 1/2` days.
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Question: A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The number of days taken in completing the work was:
A
`12 1/2`

B
`14 2/9`

C
15

D
`16 2/3`

Note: solution: Work done by A in 10 days = `(1/25 xx 10)` = `2/5`. Remaining work = `(1 - 2/5)` = `3/5`. `(A +B)`'s 1 day's work = `(1/25 + 1/20)` = `9/100`. Now, `9/100` work is done by them in 1 day. `:. 3/5` work will be done by them in `(100/9 xx 3/5) = 20/3` days. Total time taken = `(10 + 20/3)` = `16 2/3` days.
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Question: A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work, is :
A
11

B
21

C
28

D
42

Note: solution: (A's 1 day's work) : (B's 1 day's work ) =`2 : 1` `(A + B)`'s 1 day's work = `1/14`. Divide `1/14` in the ratio `2 : 1`. `:.` A's 1 day's work = `(1/14 xx 2/3 )` = `1/21`. Hence, A alone can finish the work in 21 days.
1. Report

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Question: Which of the following fractions is the smallest?

Question: 0.000006723 when expressed in scientific notation, is:

Question: What decimal of an hour is a second?

Question: If `1.125 xx 10^k = 0.001125`, then the value of k is:

Question: A and B can together finish a work in 30 days. They worked at it for 20 days and then B left. the remaining work was done by A alone in 20 more days. A alone can finish the work in :

Question: A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but a leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was :

Question: A dose half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it ?

Question: A can do a certain job in 12 days. B is 60% more efficient than A. The number of days, it take B to do the same piece of work, is :

Question: A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The number of days taken in completing the work was:

Question: A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work, is :