General Mathematics

Question: If 1 man or 2 women or 3 boys can do a piece of work in 44 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in :
A
`21` days

B
`24` days

C
`26` days

D
`33` days

Note: solution: `1` woman `-= 1/2` man `& 1` boy `-= 1/3` man. `:.`(1 man + 1 woman + 1 boy) `-= (1 + 1/2 + 1/3)` men Now, 1 man can do the work in `44` days `:. 11/6` men can do it in `(44 xx 6/11)` `= 24` days.
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Question: 8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in :
A
`10` days

B
`12` days

C
`15` days

D
`16` days

Note: solution: `1` man `-= 3/2` boys. So, (`4` men `+ 9` boys )`-= 15` boys. Also, `8` men `-= (3/2 xx 8)` boys `= 12` boys. More boys, less days. `15 : 12 :: 20 : x` `:. x = ((12 xx 20)/15)` `= 16`.
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Question: A does half as much work as B and C does half as much work as A and B together. If C alone can finish the work in 40 days, then together all will finish the work in :
A
`13 1/3` days

B
`15` days

C
`20` days

D
`30` days

Note: solution: `C`alone can finish the work in `40` days. `:. (A + B)` can do it in `20` days. `:. (A + B)'s 1` day's work `= 1/20`. `A's 1` day's work : `B's 1` day's work `= 1/2 : 1` `= 1 : 2`. `:. A's 1` day's work `= (1/20 xx 1/3)` `= 1/60`. [Divide `1/20` in the ratio 1 : 2] `B's 1` day's work `= (1/20 xx 2/3)` `= 1/30`. `(A + B + C)'s 1` day's work `= (1/60 + 1/30 + 1/40)` `= 9/120` `=3/40`. `:.` All the three together will finish it in `40/3` `=13 1/3` days.
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Question: A and B can separately do a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which C alone could do the work will be :
A
`60`

B
`40`

C
`35`

D
`30`

Note: solution: `(A + B)'s 6` day's work `= 6(1/20 + 1/15)` `= 7/10`. `(A + C)'s 4` day's work `= 3/10`. `(A + C)'s 1` day's work `= 3/40` `A's 1` day's work `= 1/20` `:. C's 1` day's work `=(3/40 - 1/20)` `=1/40`. Hence, C alone can finish the work in `40` days.
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Question: A, B and C can do a piece of work in 36, 54 and 72 days respectively. They started the work but A left 8 days before the completion of the work while B left 12 days before the completion. The number of days for which C worked is :
A
`4`

B
`8`

C
`12`

D
`24`

Note: solution: Suppose the work was finished in `x` days. Then A's `(x - 8)` day's work `+ B's (x - 12)` day's work `+ C's x` day's work `= 1` `(x - 8)/36 + (x - 12)/54 + x/72 = 1 iff 6(x - 8) + 4(x - 12) + 3x = 216` `:. 13x = 312 iff x = 24`.
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Question: Three partners A, B, C invest Rs. `36000`, Rs. `45000` and Rs. `54000` respectively in a business. Out of a total profit of Rs. `37500`, C's share is :
A
Rs. `12500`

B
Rs. `15000`

C
Rs. `10000`

D
Rs. `15500`

Note: solution: `A : B : C = 36000 : 45000 : 54000` `= 4 : 5 : 6` C's share `= Rs.(37500 xx 6/15)` `= Rs. 15000`.
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Question: Kavita and Sunita ate partners in a business. Kavita invests Rs. `35000` for `8` months ans Sunita invests Rs. `42000` for `10` months. Out of a profit of Rs.`31570`, Kavita's shate is :
A
Rs. `18942`

B
Rs. `12628`

C
Rs. `9471`

D
Rs. `18040`

Note: solution: Ratio of their shares `= 35000 xx 8 : 42000 xx 10` `= 2 : 3` Kavita's share `= Rs. (31570 xx 2/5)` `= Rs. 12628`.
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Question: jayant opened a shop investing Rs. `30000`. Madhu joined him `2` months later, investing Rs. `45000`. They earned a profit of Rs. `54000` after completion of one year. What will be Madhu's share of profit ?
A
Rs. `27000`

B
Rs. `24000`

C
Rs. `30000`

D
Rs. `36000`

Note: solution: Jayant : Madhu `= 30000 xx 12 : 45000 xx 10` `= 4 : 5`. Madhu's share `= Rs. (54000 xx 5/9)` `= Rs. 30000`.
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Question: Alok started a business investing `Rs. 90000`. After `3` months Shabir joined him with a capital of `Rs. 120000`. If at the end of `2` years, the total profit made by them was `Rs. 96000` what will be the difference between their shares ?
A
`Rs. 20000`

B
`Rs. 24000`

C
`Rs. 8000`

D
none of these

Note: solution: Alok : Shaibr `= 90000 xx 24 : 120000 xx 21` `= 6 : 7`. Difference of their shares `= Rs.(96000 xx 7/13 - 96000 xx 6/13)` `= Rs. ((96000)/13)` `= Rs. 7384.62`.
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Question: Nirmal and Kapil started a business investion `Rs. 9000` and `Rs. 12000` respectively. After `6` months, Kapil withdrew half of his investment. If after a year, the total profit was `Rs. 4600`, what was Kapil's share in it ?
A
`Rs. 2000`

B
`Rs. 2600`

C
`Rs. 1900`

D
`Rs. 2300`

Note: solution: Nirmal : Kapil `= 9000 xx 12 : 12000 xx 6 + 6000 xx 6` `= 1 : 1`. `:.` Kapil's share `=Rs. (4600 xx 1/2)` `= Rs. 2300`.
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Question: If 1 man or 2 women or 3 boys can do a piece of work in 44 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in :

Question: 8 men can dig a pit in 20 days. If a man works half as much again as a boy, then 4 men and 9 boys can dig a similar pit in :

Question: A does half as much work as B and C does half as much work as A and B together. If C alone can finish the work in 40 days, then together all will finish the work in :

Question: A and B can separately do a piece of work in 20 and 15 days respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in next 4 days, then the number of days in which C alone could do the work will be :

Question: A, B and C can do a piece of work in 36, 54 and 72 days respectively. They started the work but A left 8 days before the completion of the work while B left 12 days before the completion. The number of days for which C worked is :

Question: Three partners A, B, C invest Rs. `36000`, Rs. `45000` and Rs. `54000` respectively in a business. Out of a total profit of Rs. `37500`, C's share is :

Question: Kavita and Sunita ate partners in a business. Kavita invests Rs. `35000` for `8` months ans Sunita invests Rs. `42000` for `10` months. Out of a profit of Rs.`31570`, Kavita's shate is :

Question: jayant opened a shop investing Rs. `30000`. Madhu joined him `2` months later, investing Rs. `45000`. They earned a profit of Rs. `54000` after completion of one year. What will be Madhu's share of profit ?

Question: Alok started a business investing `Rs. 90000`. After `3` months Shabir joined him with a capital of `Rs. 120000`. If at the end of `2` years, the total profit made by them was `Rs. 96000` what will be the difference between their shares ?

Question: Nirmal and Kapil started a business investion `Rs. 9000` and `Rs. 12000` respectively. After `6` months, Kapil withdrew half of his investment. If after a year, the total profit was `Rs. 4600`, what was Kapil's share in it ?