Question
15 men can complete a work in 280 days. They started
the work and after every 10 days, 15 additional men were employed. In how many days the work was completed?Solution
Initial Men = 15. These 15 men can finish the work in 280 days. Total Work = 15 * 280 men-days days = 4200 men- days They work for 10 days. So, work done = 15*10 men-days. Now 15 more men were added, and they worked for 10 days= 30*10 men days Similarly for the next days 15*10+ 30*10+………….+ nth term = 15*280 10(15 + 30 + ..............nth term) = 15*280 So, this makes an AP. Sum= (n/2) *{2a + (n-1)d} Where n is the nth term, a= first element, d is the difference 15* 280= 10[(n/2) *{2*15 +(n-1)15}] 15*28 = (n/2)*(15+ 15n) 30*28 15n+ 15n2 n²+n = 56 So, n = 7, -8 (but n cannot be negative) So, n=7 It means 7*10 = 70 days So, work will be done in 70 days.
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...3, 49, 191, 477, ?, 1673
3 15 35 63 99 ?
Complete the series.
19, 23, 26, 30, 33, ?
4, 8, 24, ?, 840, 9240
22 15 10 20 33 93.5
...12, 23, 68, 271, 1354, ?
3 5 15 75 1125 ?
...6   55   91   116   132    ?  . Â
12, 23, 68, 271, 1354, ?
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