Multiple choice

A sum of Rs. 22000 is divided into three parts such that the corresponding interest earned after 2 years, 3 years and 6 years may be equal. If the rates of simple interest are 6% p.a., 8% p.a. and 6% p.a. respectively, what is the sum of the smaller two parts that was lent? 22000 रू. की एक धनराशि को तीन भागों में इस तरह बांटा जाता है कि उनके द्वारा क्रमशः 2 वर्षों, 3 वर्षों और 6 वर्षों में प्राप्त ब्याज समान हों। यदि साधारण ब्याज की दरें क्रमशः 6% वार्षिक 8% वार्षिक और 6% वार्षिक हैं, उधार दी गयी दो छोटी राशियों का योग क्या है?

  1. Rs. 8000

  2. Rs. 12000

  3. Rs. 10000

  4. Rs. 15000
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C Correct answer
Explanation

Set interests equal: x(2)(6) = y(3)(8) = z(6)(6). This gives 12x = 24y = 36z, so x = 2y and x = 3z. Total: x + y + z = 22000. Substituting y = x/2 and z = x/3 gives x + x/2 + x/3 = 22000, so 11x/6 = 22000, x = 12000. Then y = 6000, z = 4000. Sum of smaller two: 6000 + 4000 = 10000.

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