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.
Question:A and B can do a piece of work in 12 days ; B and C can do it in 15 days ; A and C can do it in 20 days. In how many days will A, B and C finish it, working all together ? Also, find the number of days taken by each to finish it working alone.
(A + B)'s 1 day's work` = 1/12;` (B + C)' s 1 day's work` = 1/15` and (A + C)'s 1 day's work` = 1/20` Adding, we get : 2 (A + B + C)'s 1 day's work `= (1/12 + 1/15 + 1/20) = 1/5.` :. (A + B + C)' s 1 day's work` = 1/10` Thus A,B and C together can finish the work in 10 days. Now A's 1 day's work = [(A + B + C)'s 1 day's work] - [(B + C) 's 1 day's work] `= (1/10 - 1/15) = 1/30` A alone can finish the work in 30 days. Similarly, B's 1 day's work` = (1/10 - 1/20) = 1/20` :. B alone can finish the work in 20 days. And C's 1 day's work` = (1/10 - 1/12) = 1/60. :. C alone can finish the work in 60 days.
Question:3 men can complete a piece of work in 6 days. Two days after they started the work, 3 more men joined them. How many days will they take to complete the remaining work ?
Work done by 3 men in 2 days` = (1/6 xx 2) = 1/3` Remaining work` = (1 - 1/3) = 2/3` Now 3 men's 1 day's work` = 1/6` 1 men's 1 day's work` = 1/18` 6 men's 1 day's work` = (6 xx 1/18) = 1/3` Now,` 1/3` work is done by them in 1 day. `:. 2/3` work is done by them in` (3 xx 2/3) = 2` days.
Question:2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days. In how many days can 2 men and 1 boy do the work ?
Let 1 man's 1 day's work = x & 1 boy's 1 day's work = y. Then, `2x + 3y = 1/10` and ` 3x + 2y = 1/8` Solving, we get : `x = 7/200` and` y = 1/100.` :. (2 men + 1 boy)'s 1 day's work ` = (2 xx 7/200 + 1 xx 1/100)` `= 16/200 = 2/25` So, 2 men & 1 boy together can finish the work in `25/2 = 12 1/2` days.
Question:A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work ?
(A's 1 day's work): (B's 1 day's work) = 2 : 1. (A + B)'s 1 day's work `= 1/18` Divide` 1/18` in the ratio 2 : 1. :. A's 1 day's work` = (1/18 xx 2/3) = 1/27` Hence, A alone can finish the work in 27 days.
Question:A and B undertake to do a piece of work for Rs. 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of each.
C,s 1 day's work` = 1/3 - (1/6 + 1/8) = 1/24`
:. A : B : C = Ratio of their 1 day's work
`= 1/6 : 1/8 : 1/24 = 4 : 3 : 1`
:. A's share `= Rs. (600 xx 4/8) = Rs. 300`
B's share `= Rs. (600 xx 3/8)`
`= Rs, 225.`
C,s share = Rs. [600 - (300 + 225)]`
`= Rs. 75`