4. Find the 30th term of an A.P whose first term and common difference are 3 and 5
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Answers
Answer:
Well this question falls under a particular topic known as ‘Time And Work’ and it can approached in the following manner:_
Let us suppose that in 1 day, 1 man completes ‘x’ part of the work and 1 boy completes ‘y’ part of the work.
A/Q; 2 men and 3 boys can complete the work in 10 days i.e, in 1 day they together can complete 1/10th of the work, which can be written as:
2x + 3y = 1/10
Similarly: 3 men and 2 boys can complete the work in 8 days i.e, in 1 day they can together complete 1/8th of the work, which can be written as:
3x + 2y =1/8
After simplifying both the above equations we have;
6x + 9y =3/10;
6x + 4y =2/8.
And on solving we have;
x = 7/200; y = 1/100.
So now we know the respective amount of work completed by 1 man and 1 boy in 1 day.
Therefore in 1 day, 2 men and 1 boy can complete = 2 * (7/200) + (1/100) = 2/25th of the work i.e, the whole work can be completed in 25/2 days.
Thus, the required answer is 25/2 i.e, twelve and half days.
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Tip: Well solve in the same way and the teacher can’t even dare to deduct a single mark for it, just put the implies sign before the equations.
First term(a) = 3
Common difference (d) = 5
30th term = a + 29d = 3 + 29×5 = 148