Question
- 3 men and 4 boys can earn Rs 756 in 7 days. 11 men and 13 boys can earn Rs 3008 in 8 days. In what time will 7 men with 9 boys earn Rs 2480?
Answer: Option A
Let the wages of 1 man and 1 boy be x and y respectively.
Then, according to the given conditions,
3 men and 4 boys can earn Rs 756 in 7 days
⇒ 3x + 4y = 756 (1)
11 men and 13 boys can earn Rs 3008 in 8 days
⇒ 11x + 13y = 3008 (2)
Subtracting equation (1) from equation (2), we get
8x + 9y = 2,252
⇒ x + y = 252
Now,
7 men and 9 boys can earn Rs 2480
⇒ 7x + 9y = 2480
Substituting the value of x + y+ in the above equation, we get
7x + 9y = 7(252) + 9y
⇒ 7x + 9y = 1764
Subtracting 9y from both sides, we get
7x = 1764 – 9y
⇒ x = 252 – y
Substituting the value of x in equation (1), we get
3(252 – y) + 4y = 756
⇒ 756 = 752 + y
⇒ y = 4
Therefore, the wages of 1 man and 1 boy are 252–4 = Rs 248.
Time taken by 7 men and 9 boys to earn Rs 2480
= Rs 2480/(7 × 248 + 9 × 4)
= Rs 2480/2160
= 10 days.
Hence, the correct answer is Option A: 10 days.If you think the solution is wrong then please provide your own solution below in the comments section .
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Let the wages of 1 man and 1 boy be x and y respectively.
Then, according to the given conditions,
3 men and 4 boys can earn Rs 756 in 7 days
⇒ 3x + 4y = 756 (1)
11 men and 13 boys can earn Rs 3008 in 8 days
⇒ 11x + 13y = 3008 (2)
Subtracting equation (1) from equation (2), we get
8x + 9y = 2,252
⇒ x + y = 252
Now,
7 men and 9 boys can earn Rs 2480
⇒ 7x + 9y = 2480
Substituting the value of x + y+ in the above equation, we get
7x + 9y = 7(252) + 9y
⇒ 7x + 9y = 1764
Subtracting 9y from both sides, we get
7x = 1764 – 9y
⇒ x = 252 – y
Substituting the value of x in equation (1), we get
3(252 – y) + 4y = 756
⇒ 756 = 752 + y
⇒ y = 4
Therefore, the wages of 1 man and 1 boy are 252–4 = Rs 248.
Time taken by 7 men and 9 boys to earn Rs 2480
= Rs 2480/(7 × 248 + 9 × 4)
= Rs 2480/2160
= 10 days.
Hence, the correct answer is Option A: 10 days.If you think the solution is wrong then please provide your own solution below in the comments section .
Was this answer helpful ?
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11m +4b=3,008/8......(2)
by solving eq 1 and 2
we get ;
m=20 and b=12
and puting this values in
7m+9b =2,480/x
where x us days in which 7m and 9b earn 2480 money
so we get 10 days .....
11M + 13B = 3008/8 ------ (ii)
solve the above equation (i) and (ii)
33 M+ 44 B =1,188
33 M + 39 B =1,128
------------------------------
5B = 60
:. B= 12
3 M+ 4 ×12 =108
M= 108-48/3
M = 20
we get M=20 and B=12 put these value in equation
Let X be the number of day to earn Rs.2480 by 7 men and 9 boys
7M + 9B = (2480/X) put the value of M and
7 M + 9 B= 2480 / X
7×20 + 9×12 = 2480 / X
X = 10
we get X=10 Days
(3m+4b)1d=108. eq _ (1)
(11m+13b)8d=3008
(11m+13b)1d=376. eq_(2)
Solve eq(1)&(2)
1b=12
1m=20
(7m+9b)1d= 7*20+9*12=248
(7m+9b)10d=2480
Ans=10d