Two equal sums of money are lent at the same time at 8% and 7% per annum simple interest. The former is recovered 6 months earlier than the later and the amount in each case is Rs. 2560. The sum and time for which the sums of money are lent out are
A
Rs. 1500,3.5 year and 4 year
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B
Rs. 2000,3.5 years and 4 years
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C
Rs. 2000,4 years and 5.5 years
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D
Rs. 3000,4 years and 4.5 years
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Solution
The correct option is D Rs. 2000,3.5 years and 4 years Let the sum be Rs. x. Therefore, Rs. x are lent at 8% for t years and Rs. x are lent at 7% for (t+12) years. ∴x×t×8100+x=2560 ⇒8tx+100x=256000 .....(i) and x×(2t+1)×72×100+x=2560 ⇒14tx+7x+200x200=2560 ⇒14tx+207x=512000 .....(ii) Performing (i) ×7− (ii) ×4, we get (56tx+700x)−(56tx+828x)=256000×7−512000×4 ⇒700x−828x=1792000−2048000 ⇒120x=256000
⇒x=2000 Putting the value of x in (i), we get 8×t×2000+100×2000=256000 ⇒16000t=256000−200000 ⇒16000t=56000