Work and Wages
- Men, women and children are employed to do a work in the proportion of 3 : 2 : 1 and their wages as 5 : 3 : 2. When 90 men are employed, total daily wages of all amounts to ₹ 10350. Find the daily wages of a man.
-
View Hint View Answer Discuss in Forum
Let the numbers of men, women and
children are 3k, 2k and k, respectively.
Given, 3k = 90
⇒ k = 30
Number of women = 60
and number of children = 30
Let the men's, women's and children's
wages be ₹ 5p, ₹ 3p and ₹ 2p, respectively.
According to the question,
Total daily wages = ₹ 10350
⇒ 90 x 5p + 60 x 3p + 30 x 2p = 10350Correct Option: D
Let the numbers of men, women and
children are 3k, 2k and k, respectively.
Given, 3k = 90
⇒ k = 30
Number of women = 60
and number of children = 30
Let the men's, women's and children's
wages be ₹ 5p, ₹ 3p and ₹ 2p, respectively.
According to the question,
Total daily wages = ₹ 10350
⇒ 90 x 5p + 60 x 3p + 30 x 2p = 10350
⇒ p x (450 + 180 + 60) = 10350
∴ p = 10350/690 = 15
∴ Daily wages of a man = 15 x 5 = ₹ 75
- 2 men and 1 woman can do a piece of work in 14 days, while 4 women and 2 men can do the same work in 8 days. If a men gets ₹ 90 per day, what should be the wages per day of a women?
-
View Hint View Answer Discuss in Forum
Let man be represented by m and woman be represented by w.
∵ 2m + 1w = 1/14
⇒ 14 x (2m + 1w ) = 1 ...(i)
and 4w + 2m = 1/8
8 x (4w + 2m) = 1 ...(ii)
On equating Eqs. (i) and (ii), we get
14 (2m + 1w) = 8 (4w + 2m)Correct Option: B
Let man be represented by m and woman be represented by w.
∵ 2m + 1w = 1/14
⇒ 14 x (2m + 1w ) = 1 ...(i)
and 4w + 2m = 1/8
8 x (4w + 2m) = 1 ...(ii)
On equating Eqs. (i) and (ii), we get
14 (2m + 1w) = 8 (4w + 2m)
⇒ 28m + 14w = 32w + 16m
⇒ 28m - 16m = 32w - 14w
⇒ 12m = 18w
∴ m/w = 18/12 = 3/2
So, efficiency of 1 man and 1 woman is 3 : 2.
So, their wages must be in the same ratio
90/x = 3/2
[here, x = wages of a woman ]
∴ x = 90 x 2 / 3 = ₹ 60
- Total wages for a work is ₹ 1280. A alone can do a piece of work in 8 days, while B alone can do it in 12 days. If A and B work on alternate days, then find the share of A.
-
View Hint View Answer Discuss in Forum
Work for 1 st 2 days = (1/8) + (1/12) = 5/24
∴ Work for 8 days = (5/24) x (8/2) = 5/6
∴ Remaining work = 1- (5/6) = (6 - 5) / 6 = 1/6
On 9th day, A's work = 1/8
Remaining work after 9 days = (1/6) - (1/8) = (4 - 3) / 24 = 1/24
B will finish this work in (12 x 1)/24 = 1/2 day
Clearly, A worked for 5 days from starting.Correct Option: A
Work for 1 st 2 days = (1/8) + (1/12) = 5/24
∴ Work for 8 days = (5/24) x (8/2) = 5/6
∴ Remaining work = 1- (5/6) = (6 - 5) / 6 = 1/6
On 9th day, A's work = 1/8
Remaining work after 9 days = (1/6) - (1/8) = (4 - 3) / 24 = 1/24
B will finish this work in (12 x 1)/24 = 1/2 day
Clearly, A worked for 5 days from starting.
∴ Work done by A in 5 days = (1/8) x 5 = 5/8
∴ A's share = (5/8) x 1280 = 5 x 160 = ₹ 800
- 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?
-
View Hint View Answer Discuss in Forum
∵ 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?
-
View Hint View Answer Discuss in Forum
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.
