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Daily earnings of two persons are in the ratio 4:5 and their daily expenses are in the ratio 7 : 9. If each saves Rs. 50 per day, their daily incomes in Rs. are
- a)(40, 50)
- b)(50, 40)
- c)(400, 500)
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Daily earnings of two persons are in the ratio 4:5 and their daily exp...
Let the monthly income of one person be 4x and that of the other be 5x
Let the monthly expenses of one person be 7y and that of other be 9y
ATQ
4x-7y=50-(1)-*5=20x-35y=250
5x-9y=50-(2)-*4=20x-36y=200
=y=50
from 1
4x-7*50=50
4x=50+350
4x=400
x=100
Monthly income of one person=4x=4*100=400
Monthly income of the other person=5x=5*100=500
Most Upvoted Answer
Daily earnings of two persons are in the ratio 4:5 and their daily exp...
Given: Ratio of daily earnings of two persons = 4:5
Ratio of their daily expenses = 7:9
Each saves Rs. 50 per day.
To find: Daily incomes of two persons.
Solution:
Let the daily earnings of two persons be 4x and 5x respectively.
Let the daily expenses of two persons be 7y and 9y respectively.
According to the problem, each saves Rs.50 per day.
Therefore, the daily savings of the first person = 4x - 7y - 50
The daily savings of the second person = 5x - 9y - 50
Since the savings of both the persons are equal, we get:
4x - 7y - 50 = 5x - 9y - 50
⇒ x = 2y
Substituting the value of x in terms of y in the expressions for daily earnings, we get:
Daily earnings of the first person = 4x = 8y
Daily earnings of the second person = 5x = 10y
Hence, the daily incomes of the two persons are 8y and 10y respectively.
Given ratio of daily expenses of two persons = 7:9
⇒ (7y)/(9y) = 7/9
⇒ 7y = (7/9) × 9y = (7/9) × (5x - 50) = (35/9)x - (350/9)
⇒ y = (5/9)x - (50/7)
Substituting the value of x in terms of y, we get:
y = (5/9) × 2y - (50/7)
⇒ (7/9)y = - (50/7)
⇒ y = - (50 × 9)/(7 × 9)
⇒ y = - 50/7
However, since expenses cannot be negative, we discard this value.
Therefore, the given problem has no solution.
Hence, the correct option is (d) None of these.
Ratio of their daily expenses = 7:9
Each saves Rs. 50 per day.
To find: Daily incomes of two persons.
Solution:
Let the daily earnings of two persons be 4x and 5x respectively.
Let the daily expenses of two persons be 7y and 9y respectively.
According to the problem, each saves Rs.50 per day.
Therefore, the daily savings of the first person = 4x - 7y - 50
The daily savings of the second person = 5x - 9y - 50
Since the savings of both the persons are equal, we get:
4x - 7y - 50 = 5x - 9y - 50
⇒ x = 2y
Substituting the value of x in terms of y in the expressions for daily earnings, we get:
Daily earnings of the first person = 4x = 8y
Daily earnings of the second person = 5x = 10y
Hence, the daily incomes of the two persons are 8y and 10y respectively.
Given ratio of daily expenses of two persons = 7:9
⇒ (7y)/(9y) = 7/9
⇒ 7y = (7/9) × 9y = (7/9) × (5x - 50) = (35/9)x - (350/9)
⇒ y = (5/9)x - (50/7)
Substituting the value of x in terms of y, we get:
y = (5/9) × 2y - (50/7)
⇒ (7/9)y = - (50/7)
⇒ y = - (50 × 9)/(7 × 9)
⇒ y = - 50/7
However, since expenses cannot be negative, we discard this value.
Therefore, the given problem has no solution.
Hence, the correct option is (d) None of these.
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Daily earnings of two persons are in the ratio 4:5 and their daily expenses are in the ratio 7 : 9. If each saves Rs. 50 per day, their daily incomes in Rs. area)(40, 50)b)(50, 40)c)(400, 500)d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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