General Mathematics

Question: A gain dealer cheats to the extent of 10 % while buying as well as selling, by using false weights. His total gains is :
A10 %

B20 %

C`22 2/9` %

D21 %

Note: We know,  Gain % = `(100 + commongain % )^2/100` - 100

Gain % = `((100 + 10 )^2/100 - 100)` %

= `((12100 -10000)/100)` % 
= 21 %

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Question: Toffees bought at the rate of 3 for a taka. to gain 50 %, they must be sold at
A2 for a taka

B1 for a taka

C4 for a taka

D5 for a taka

Note: C.P of 3 toffees = Tk 1
S.P of 3 toffees = 150 % of  Tk 1 = Tk `3/2`
For taka `3/2`, toffees sold = 3
For taka 1, toffees sold = `(3 xx 2/3)` 
    = 2

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Question: By selling toffees at 20 for a taka, a man loses 4 %. To gain 20 % for 1 taka, he must sell
A16 toffees

B20 toffees

C24 toffees

D25 toffees

Note: Let S.P of 20 toffees be tk x. 
then, 96 : 1 = 120 : x
or, x = `(120)/96`
= `5/4`
For taka `5/4`, toffees sold = 20
For taka 1, toffees sold = `(20 xx 4/5)` 
    =16

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Question: A and B together can complete a piece of work in 35 days while A alone can complete the same work in 60 days. B alone will be able to complete the same work in :
A42 days

B72 days

C84 days

D96 days

Note: solution:
(A + B)'s  1 day's work = `1/35` 
     & A's 1 day's work = `1/60`.
`:.` B's 1 day's work = `(1/35 - 1/60)`
                      = `5/420`
                      = `1/184`.
Hence B alone will finish the work in 84 days.

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Question: A can do a piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together 8 2/5 hours a day ?
A3 days

B4 days

C4 1/2 days

DNone of these

Note: solution:
A  can complete the work in `(7 xx 9)` hrs = 63 hrs.
B can complete the work in  `(6 xx 7)` hrs = 42 hrs.
 `:.` A's 1 hour's work = `1/63` 
    &  B's 1 hour's work = `1/42`.
`(A + B)`'s 1 hour's work = `(1/63 + 1/42)`
                         = `5/126`.
`:.` Both will finish the work in `(126/5)` hrs.
Number of days of `8 2/5` hrs each =  `(126/5 xx 5/42)`
                                  =  3 days.

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Question: Which of the following sets of fractions is in ascending order?
A`5/6,6/8,7/9,11/13`

B`6/8,7/9,5/6,11/13`

C`11/13,5/6,7/9,6/8`

D`11/13,7/9,6/8,5/6`

Note: Converting each into decimal form, we get:
`5/6=0.833,6/8=0.75,7/9=0.777,11/13=0.846.`
Clearly, `0.75<0.777<0.833<0.846` or `6/8<7/9<5/6<11/13.`

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Question: A can do a piece of work in 15 days and B alone can do it in 10 days. B work at it for 5 days and then leaves. A alone can finish the remaining work in :
A`6 1/2` days

B`7 1/2` days

C8 days

D9 days

Note: solution:
B's 5 day's work = `(1/10 xx 5)`
                           = `1/2`.
Remaining work = `(1 - 1/2)`
                          = `1/2`.
A can do `1/2` work in `7 1/2` days.

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Question: A can do `1/3` of the work in 5 days and B can do `2/5` of the work in 10 days. In how many days both A and B together can do the work ?
A`7 3/4`

B`8 4/5`

C`9 3/8`

D10

Note: solution:
Whole work will be done by A in `(5 xx 3)`
                                   = `15` days.
Whole work will be done by B in `(10 xx 5/2)`
                                   = `25` days.
A's 1 day's work = `1/15` &
 B's 1 day's work = `1/25`.
`(A + B)`'s 1 day's work = `(1/15 + 1/25)`
                                       = `8/75`.
So, both together can finish it in `75/8`
                                    =`9 3/8` days.

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Question: A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. The two together could complete the work in :
A24 days

B25 days

C30 days

D35 days

Note: solution:
Work done by A in 10 days = `(1/80 xx 10)` 
                                           = `1/8`.
Remaining work =`(1 - 1/8)`
                          = `7/8`.
Now, `7/8` work is done by B in 42 days
Whole work will be done by B in `(42 xx 8/7)`
                                                    = 48 days.
`:.` A's 1 day's work = `1/80` &
      B's 1 day's work = `1/48`.
`:. (A + B)`'s 1 day's work =`(1/80 + 1/48)`
                                        =`8/240`
                                        =`1/30`.
Hence, both will finish the work in 30 days.

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Question: Which part contains the fractions in ascending order?
A`11/14,16/19,19/21`

B`16/19,11/14,19/21`

C`19/21,11/14,16/19`

D`16/19,19/21,11/14`

Note: Converting each into decimal form, we get:
`11/14=0.785,16/19=0.842` & `19/21=0.904.`
Clearly, 0.785<0.842<0.904` or `11/14<16/19<19/21.`

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