Simple Interest [साधारण ब्याज-04

Question: A man had Rs. 2000, part of which he lent at 5% and the rest at 4%. The whole annual interest is Rs. 92. The money he lent at 5% was…..   [एक व्यक्ति के पास 2000 रु थे; जिसका एक भाग उसने 5% की दर से तथा शेष भाग उसने 4% की दर से लगाया. यदि उसे वार्षिक साधारण ब्याज 92 रु मिला हो, तो बताएं कि 5% की दर पर, उसने कितना धन लगाया था?]        [Ans. (c) (Rs. 1200)]

(a) Rs. 1000      (b) Rs. 1500       (c) Rs. 1200       (d) Rs. 2000       (e) none of these

Solution:

  

Detailed Explanation: We can solve this problem by method of “Alligation”. Method of Alligation can be used by two ways.

First Method: By method of Alligation, one part of the total sum of Rs.2000 is invested at the simple interest rate of 5% pan; while another part, at the simple interest rate of 4% pan. Here, the rate is taken as per hundred. In one year the SI is Rs. 92, which is 4.6% of Rs. 2000 and this, is the mean rate.

Ratio of investments at 5% and 4% is = (92-80) : (100-92) = 12 : 8 = 3 : 2

     Total investment = 5 ≡ 2000

(Investment at 5% pan) = 3 ≡? = 1200 Ans.     

                                 By method of Alligation          

                                                      Rs. 2000     

                                      I (%/pan)             II (%/pan) 

                                           5                              4     

                                                Mean (%/pan)

                                                (92×100)÷2000

                                                       = 4.6 

                                      0.6 (4.6-4)     :        0.4 (5-4.6)

                                    Or,   3             :           2 

           

     Total investment = 5 ≡ 2000

(Investment at 5% pan) = 3 ≡? = 1200 Ans.     

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Second Method: By method of Alligation, one part of the total sum of Rs.2000 is invested at the simple interest rate of 5% pan; while another part, at the simple interest rate of 4% pan. Here, the rate is taken as per hundred. In one year the SI is Rs. 92, which is 4.6% of Rs. 2000 and this, is the mean rate.

Ratio of investments at 5% and 4% is = (92-80) : (100-92) = 12 : 8 = 3 : 2

     Total investment = 5 ≡ 2000

(Investment at 5% pan) = 3 ≡? = 1200 Ans.     

            Second Method

        By method of Alligation

                     Rs. 2000

        I (1/2000)             II (1/2000)                                 

            100                        80 

                Mean (1/2000)

                         92

          12 (92-80):        8 (100-92) 

             or, 3       :        2     

Total investment = 5 ≡ 2000

(Investment at 5% pan) = 3 ≡? = 1200 Ans.     

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Third Method : Let the part of Rs. 2000 invested at the simple interest rate of 5% pan is Rs. “x”; then the other part of Rs.2000 is Rs. (2000-x), which is invested at the simple interest rate of 4% pan. Since the annual interest from both the parts together is Rs. 92, so

5% of x + 4% of (2000-x) = 92

1% of x = 12

100%of x = Rs. 1200 Ans.