A bag contains some one-rupee coins and some fifty-paisa coins. The total amount is ₹ 140. If half of the one-rupee coins are replaced by fifty-paisa coins, then the amount becomes ₹ 115. The coins of each type in the bag initially, were : 1. one-rupee coins = 100 and fifty-paisa coins = 80 2. one-rupee coins = 80 and fifty-paisa coins = 100 3. one-rupee coins = 110 and fifty-paisa coins = 80 4. one-rupee coins = 70 and fifty-paisa coins = 90

Let x be the number of one rupee coins and y be the number of 50 paisa coins in the bag initially. Given, Initial total amount = ₹ 140. ⇒ x + 0.5y = 140 ⇒ x = 140 - 0.5y .......(1) Given, After replacing half of the 1-rupee coins with 50-paisa coins, the amount becomes ₹ 115. ⇒ + 0.5y + 0.5 = 115 ⇒ 0.5x + 0.5y + 0.25x = 115 ⇒ 0.75x + 0.5y = 115 ........(2) Substituting value of x from equation (1) in (2), we get : ⇒ 0.75(140 - 0.5y) + 0.5y = 115 ⇒ 105 - 0.375y + 0.5y = 115 ⇒ 0.125y = 115 - 105 ⇒ 0.125y = 10 ⇒ y = = 80. Substituting value of y in equation (1), we get : ⇒ x = 140 - 0.5y ⇒ x = 140 - 0.5(80) ⇒ x = 140 - 40 ⇒ x = 100. ∴ Number of one rupee coins = 100 and number of fifty paisa coins = 80. Hence, option 1 is the correct option.

Mathematics

A bag contains some one-rupee coins and some fifty-paisa coins. The total amount is ₹ 140. If half of the one-rupee coins are replaced by fifty-paisa coins, then the amount becomes ₹ 115. The coins of each type in the bag initially, were :
one-rupee coins = 100 and fifty-paisa coins = 80
one-rupee coins = 80 and fifty-paisa coins = 100
one-rupee coins = 110 and fifty-paisa coins = 80
one-rupee coins = 70 and fifty-paisa coins = 90

Linear Equations

1 Like

Answered By

1 Like

Mathematics

Linear Equations

Related Questions

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Then the original number is :
90
18
81
54

Five years ago, Bharat was thrice as old as Rajat. Ten years later, Bharat will be twice as old as Rajat. The difference between their present ages is :
10 years
20 years
30 years
35 years

Mathematics

Linear Equations

Related Questions

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Then the original number is :90188154

Five years ago, Bharat was thrice as old as Rajat. Ten years later, Bharat will be twice as old as Rajat. The difference between their present ages is :10 years20 years30 years35 years

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Then the original number is :
90
18
81
54

Five years ago, Bharat was thrice as old as Rajat. Ten years later, Bharat will be twice as old as Rajat. The difference between their present ages is :
10 years
20 years
30 years
35 years