UPSC Prelims 2011·CSAT·Quantitative Aptitude·Arithmetic

A person has only Rs. 1 and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs. 75, then the number of Rs. 1 and Rs. 2 coins are, respectively

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  1. A15 and 35
  2. B35 and 15
  3. C30 and 20
  4. D25 and 25Correct

Explanation

Let x be the number of Rs. 1 coins and y be the number of Rs. 2 coins. From the problem statement, we can form two equations: 1. Total number of coins is 50: x + y = 50 2. Total amount of money is Rs. 75: 1x + 2y = 75 Now, we solve this system of equations. From the first equation, we can express x as x = 50 - y. Substitute this value of x into the second equation: (50 - y) + 2y = 75 50 + y = 75 y = 75 - 50 y = 25 Now substitute y = 25 back into the first equation: x + 25 = 50 x = 50 - 25 x = 25 So, the number of Rs. 1 coins is 25 and the number of Rs. 2 coins is 25. Analyzing the options: A) 15 and 35: Total coins = 15+35=50. Total amount = 1*15 + 2*35 = 15+70 = 85 (Incorrect) B) 35 and 15: Total coins = 35+15=50. Total amount = 1*35 + 2*15 = 35+30 = 65 (Incorrect) C) 30 and 20: Total coins = 30+20=50. Total amount = 1*30 + 2*20 = 30+40 = 70 (Incorrect) D) 25 and 25: Total coins = 25+25=50. Total amount = 1*25 + 2*25 = 25+50 = 75 (Correct) Therefore, option D is correct.
Quantitative Aptitude: A person has only Rs. 1 and Rs. 2 coins with her. If the total number of coins that she has is 50 and the amount of mone
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