Name: Finding the nth Term of A.P. With Given Two Terms
Uploaded: 2019-07-19
Duration: 2 min 38 s
Description: Add the common difference to the first term to get the second term. Add the common difference to the second term to get the third term. Continue to identify...

Question

A man is employed to count

₹ 10710

. He counts at the rate of

₹ 180

per minute for half an hour. After this he counts at the rate of

₹ 3

less every minute than the preceding minute. Find the time taken by him to count the entire amount.

Accepted Answer

In the given problem, the total amount $= ₹ 10710$ .

For the first half and hour ( $30$ minutes) he counts at a rate of $₹ 180$ per minute.

So, the amount counted in $30$ minutes $= (180) (30) = ₹ 5400$

So, amount left after half an hour $= 10710 - 5400 = ₹ 5310$

After $30$ minutes he counts at a rate of $₹ 3$ less every minute.

So, at $31$ minute the rate of counting per minute $= 177$ .

At $32$ minute the rate of counting per minute $= 174$ .

So, the rate of counting per minute for each minute will form an A.P. with the first term as $177$ .

And common difference $(d) = 174 - 177 = - 3$ .

So, the total time taken to count the amount left after half an hour can be calculated by using the formula for the sum of $n$ terms of an A.P.,

$S_{n} = \frac{n}{2} [2 a + (n - 1) d]$

We get,

$5310 = \frac{n}{2} [2 (177) + (n - 1) (- 3)] . . . . (1)$

$\Rightarrow 5310 (2) = n [354 - 3 n + 3]$

$\Rightarrow 10620 = n (357 - 3 n)$

$\Rightarrow 10620 = 357 n - 3 n^{2}$

So, we get the following quadratic equation,

$3 n^{2} - 357 n + 10620 = 0$

$\Rightarrow n^{2} - 119 n + 3540 = 0$

Solving the equation by splitting the middle term, we get,

$n^{2} - 60 n - 59 n + 3540 = 0$

$\Rightarrow n (n - 60) - 59 (n - 60) = 0$

$\Rightarrow (n - 60) (n - 59) = 0$

So,

$n - 59 = 0$

$\Rightarrow n = 59$

So, we will take $n = 59$ .

Therefore, the total time required for counting the entire amount $= 30 + 59$ minutes $= 89$ minutes.

So, the total time required for counting the entire amount is $89$ minutes.

A man is employed to count $₹ 10710$ . He counts at the rate of $₹ 180$ per minute for half an hour. After this he counts at the rate of $₹ 3$ less every minute than the preceding minute. Find the time taken by him to count the entire amount.

Important Questions on Arithmetic Progression

Learn and Prepare for any exam you want !

A man is employed to count ₹10710. He counts at the rate of ₹180 per minute for half an hour. After this he counts at the rate of ₹3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.

Important Questions on Arithmetic Progression

Learn and Prepare for any exam you want !

A man is employed to count $₹ 10710$ . He counts at the rate of $₹ 180$ per minute for half an hour. After this he counts at the rate of $₹ 3$ less every minute than the preceding minute. Find the time taken by him to count the entire amount.