Work and Wages
- A man and a boy received $800 as wages for 5 days for the work they did together. The man’s efficiency in the work was three times that of the boy. What are the daily wages of the boy?
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According to question , we can say that
1 man = 3 boys
Given :- Wages for five days = $800 and Total received payment = $800∴ Wages for one day = 800 = $ 160 5
The wages of $160 are to be divided among the man and boy in the ratio 1 : 3.∴Wages of the boy per day = $ 
Boy 's ratio x Total payment 
Sum of both ratios Correct Option: D
According to question , we can say that
1 man = 3 boys
Given :- Wages for five days = $800 and Total received payment = $800∴ Wages for one day = 800 = $ 160 5
The wages of $160 are to be divided among the man and boy in the ratio 1 : 3.∴Wages of the boy per day = $ Boy 's ratio x Total payment Sum of both ratios ∴ Wages of the boy per day = 1 x 160 = $ 40 4
- 4 men and 6 woman get ₹ 1600 by doing a piece of work in 5 days. 3 men and 7 women get ₹ 1740 by doing the same work in 6 days. In how many days, 7 men and 6 women can complete the same work getting ₹ 3760?
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∵ In 5 days , (4 men + 6 women ) get ₹ 1600.
∴ In 1 day, (4 men + 6 women) get ₹ 1600/5 = ₹ 320 ....(i)
In 1 day number of person to get ₹ 1 = 320 / 4 men + 6 women ....(ii)
Similarly, in second condition,
In 1 day, number of person to get ₹ 1 = (1740 / 6) x (3 men + 7 women)
= 290 / (3 men + 7 women) ....(iii)
From Eqs. (ii) and (iii), we get
320 / (4 men + 6 women) = 290 / (3 men + 7 women)
96 men + 224 women = 116 men + 174 womenCorrect Option: B
∵ In 5 days , (4 men + 6 women ) get ₹ 1600.
∴ In 1 day, (4 men + 6 women) get ₹ 1600/5 = ₹ 320 ....(i)
In 1 day number of person to get ₹ 1 = 320 / 4 men + 6 women ....(ii)
Similarly, in second condition,
In 1 day, number of person to get ₹ 1 = (1740 / 6) x (3 men + 7 women)
= 290 / (3 men + 7 women) ....(iii)
From Eqs. (ii) and (iii), we get
320 / (4 men + 6 women) = 290 / (3 men + 7 women)
96 men + 224 women = 116 men + 174 women
⇒ 20 men = 50 women
⇒ Man / Women = 5/2
∴ 1 women = 2/5 man
From Eq. (i), 1 day,
(4 men + 6 women) = (4 men + 6 x 2/5 men) = 32/5 men get ₹ 320
∴ In 1 day, 1 man get = 320 x 5 /32 = ₹ 50
∴ In 1 day, 1 woman get = 50 x 2/5 = ₹ 20
∴ In 1 day, (7 men + 6 women) get
7 x 50 + 6 x 20 = ₹ 470
∴ Required number of days = 3760 / 470 = 8 days
- The first man alone can complete this work in 7 days. The second man alone can do this work in 8 days. If they are working together to complete this work in 3 days and also taking help of a boy, then how should the money be divided?
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As we know that ,
Given :- Total money = $1400
Wages of the first man for 3 days = work done by him in 3 days × $1400Wages of the first man for 3 days = 3 × 1400 = $600 7
Wages of second man for 3 days = work done by him in 3 days × $1400Wages of second man for 3 days = 3 × 1400 = $525 8
∴ Wages of the boy for 3 days = $1400 - $( 600 + 525 ) = $275
Correct Option: B
As we know that ,
Given :- Total money = $1400
Wages of the first man for 3 days = work done by him in 3 days × $1400Wages of the first man for 3 days = 3 × 1400 = $600 7
Wages of second man for 3 days = work done by him in 3 days × $1400Wages of second man for 3 days = 3 × 1400 = $525 8
∴ Wages of the boy for 3 days = $1400 - $( 600 + 525 ) = $275
∴ Their shares will be $600, $525 and $275, respectively.
- Two men undertake a piece of work for $600. Individually, they can complete the work in 6 days and 8 days, respectively. With the assistance of a boy they completed the work in 3 days. The boy’s share should be:
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According to question , we have
Given that :- Total received payment = $600The first man’s 3 days’ work = 3 = 1 6 2 The second man’s 3 days’ work = 3 8 The boy’s 3 days’ work = 1 - 1 + 3 = 1 2 8 8 ∴ They should get money in the ratio = 1 : 3 : 1 = 4 : 3 : 1 2 8 8 ∴ The boy’s share = $ Boy 's ratio x Total amount Sum of all ratios Correct Option: C
According to question , we have
Given that :- Total received payment = $600The first man’s 3 days’ work = 3 = 1 6 2 The second man’s 3 days’ work = 3 8 The boy’s 3 days’ work = 1 - 1 + 3 = 1 2 8 8 ∴ They should get money in the ratio = 1 : 3 : 1 = 4 : 3 : 1 2 8 8 ∴ The boy’s share = $ Boy 's ratio x Total amount Sum of all ratios ∴ The boy’s share = $ 1 x 600 = $ 75 8
- A and B undertook to do a piece of work for $4500. A alone could do it in 8 days and B alone in 12 days. With the assistance of C they finished the work in 4 days. Then C’s share of the money is:
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As we know that ,
Given that :- Total Payment = $4500C alone can do the work in 1 - 1 + 1 = 1 - 5 = 6 - 5 = 1 i.e., 24 days 4 8 12 4 24 24 24 Ratio of wages = 1 : 1 : 1 : = 3 : 2 : 1 8 12 24 C’s share = C’s ratio × Total amount Sum of all ratios
Correct Option: C
As we know that ,
Given that :- Total Payment = $4500C alone can do the work in 1 - 1 + 1 = 1 - 5 = 6 - 5 = 1 i.e., 24 days 4 8 12 4 24 24 24 Ratio of wages = 1 : 1 : 1 : = 3 : 2 : 1 8 12 24 C’s share = C’s ratio × Total amount Sum of all ratios C’s share = 1 × 4500 = $750. 6
