Question:Simple interest on a certain sum is `16/25` of the sum. Find the rate percent and time, If both are numerically equal.
Let sum = x. Then, S.I = `(16x)/25` Let rate = R % and time = R years. `:. (x xx R xx R)/(100)` `= (16x)/25 or R^2 = (1600)/25 R = 40/5 = 8` :. Rate = 8% and Time = 8 years.
Question:A man borrowed Rs 24000 from two money Ienders. For one loan, he paid 15% per annum and for the other 18% per annum. At the end of one year, he paid Rs. 4050. How much did he borrow at each rate ?
Let the sum at 15% be Rs x and that at 18% be Rs (24000 - x). `:. (x xx 15 xx 1)/(100) + ((24000 - x) xx 18 xx 1)/(100)` `= 4050` `or 15x + 432000 - 18x` `= 405000 or x = 9000.` :. Money borrowed at 18% = Rs. 15000.
Question:What annual installment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest ?
Let each installment be Rs. x. then `(x + (x xx 12 xx 1)/(100)) + (x + (x xx 12 xx 2)/(100)) + x` `= 1092` `or (28x)/25 + (31x)/25 + x` `= 1092 or (28x + 31x + 25x)` `= (1092 xx 25)` `or x = ((1092 xx 25)/(84))` `= 325.` :. Each installment = Rs. 325
Question:A can do a piece of work in 10 days which B done can do in 12 days. In how many days will they finish the work, both working together ?
A's 1 day's work` = 1/10,` B's 1 day's work` = 1/2` (A + B)'s 1 day's work` = (1/10 + 1/12) = 11/60`. :. Both will finish the work in` 60/11 = 5 5/11` days.
Question:Two persons A and B working together can dig a trench in 8 hours while A alone can dig it in 12 hours. In how many hours B alone can dig such a trench ?
(A + B)'s 1 hour' s work `= 1/8` A's 1 hour's work `=1/12` :. B' s 1 hour's work` = (1/8 - 1/12) = 1/24` Hence B alone can dig the trench in 24 hours.