Advertisements
Advertisements
Question
Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount. How much the scooter will cost him.
Advertisements
Solution
Cost of the scooter = Rs 22000
Shamshad Ali pays Rs 4000 in cash.
∴ Unpaid amount = Rs 22000
\[-\] Rs 4000 = Rs 18000
Number of years taken by Shamshed Ali to pay the whole amount = 18000
\[\div\] 1000 = 18
He agrees to pay the balance in annual instalments of Rs 1000 plus 10% interest on the unpaid amount.
Total amount of instalments:
10 % of Rs 18000 + 10 % of Rs 17000 + 10 % of Rs 16000
\[ = 1800 + 1700 + 1600 . . . . \]
It is in an A.P. where a = 1800, d = \[-\] 100 and n = 18.
Therefore, total amount of instalments:
\[\frac{18}{2}\left[ 2 \times 1800 + (18 - 1) \times - 100 \right]\]
\[ = 9\left[ 3600 - 1700 \right]\]
\[ = \text { Rs } 17100\]
∴ Total amount Shamshad Ali has to pay = Rs (22000 + 17100) = Rs 39100
RELATED QUESTIONS
In an A.P., if pth term is 1/q and qth term is 1/p, prove that the sum of first pq terms is 1/2 (pq + 1) where `p != q`
If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term
Sum of the first p, q and r terms of an A.P. are a, b and c, respectively.
Prove that `a/p (q - r) + b/q (r- p) + c/r (p - q) = 0`
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
Find the sum of all numbers between 200 and 400 which are divisible by 7.
If the sequence < an > is an A.P., show that am +n +am − n = 2am.
Which term of the A.P. 3, 8, 13, ... is 248?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely real ?
Which term of the sequence 12 + 8i, 11 + 6i, 10 + 4i, ... is purely imaginary?
If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.
Find the 12th term from the following arithmetic progression:
3, 8, 13, ..., 253
The first and the last terms of an A.P. are a and l respectively. Show that the sum of nthterm from the beginning and nth term from the end is a + l.
Three numbers are in A.P. If the sum of these numbers be 27 and the product 648, find the numbers.
Find the sum of the following arithmetic progression :
50, 46, 42, ... to 10 terms
Find the sum of the following serie:
(a − b)2 + (a2 + b2) + (a + b)2 + ... + [(a + b)2 + 6ab]
How many terms of the A.P. −6, \[- \frac{11}{2}\], −5, ... are needed to give the sum −25?
If S1 be the sum of (2n + 1) terms of an A.P. and S2 be the sum of its odd terms, then prove that: S1 : S2 = (2n + 1) : (n + 1).
If the sum of n terms of an A.P. is nP + \[\frac{1}{2}\] n (n − 1) Q, where P and Q are constants, find the common difference.
If \[\frac{b + c}{a}, \frac{c + a}{b}, \frac{a + b}{c}\] are in A.P., prove that:
\[\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\] are in A.P.
If a, b, c is in A.P., prove that:
(a − c)2 = 4 (a − b) (b − c)
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
A man saves Rs 32 during the first year. Rs 36 in the second year and in this way he increases his savings by Rs 4 every year. Find in what time his saving will be Rs 200.
A man accepts a position with an initial salary of ₹5200 per month. It is understood that he will receive an automatic increase of ₹320 in the very next month and each month thereafter.
(i) Find his salary for the tenth month.
(ii) What is his total earnings during the first year?
If the sums of n terms of two arithmetic progressions are in the ratio 2n + 5 : 3n + 4, then write the ratio of their m th terms.
Write the sum of first n even natural numbers.
Write the value of n for which n th terms of the A.P.s 3, 10, 17, ... and 63, 65, 67, .... are equal.
If \[\frac{3 + 5 + 7 + . . . + \text { upto n terms }}{5 + 8 + 11 + . . . . \text { upto 10 terms }}\] 7, then find the value of n.
If the sums of n terms of two AP.'s are in the ratio (3n + 2) : (2n + 3), then find the ratio of their 12th terms.
Sum of all two digit numbers which when divided by 4 yield unity as remainder is
If Sn denotes the sum of first n terms of an A.P. < an > such that
The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
Let Sn denote the sum of n terms of an A.P. whose first term is a. If the common difference d is given by d = Sn − k Sn − 1 + Sn − 2 , then k =
If second, third and sixth terms of an A.P. are consecutive terms of a G.P., write the common ratio of the G.P.
If there are (2n + 1) terms in an A.P., then prove that the ratio of the sum of odd terms and the sum of even terms is (n + 1) : n
The product of three numbers in A.P. is 224, and the largest number is 7 times the smallest. Find the numbers
A man accepts a position with an initial salary of Rs 5200 per month. It is understood that he will receive an automatic increase of Rs 320 in the very next month and each month thereafter. What is his total earnings during the first year?
If the sum of n terms of an A.P. is given by Sn = 3n + 2n2, then the common difference of the A.P. is ______.
If a1, a2, a3, .......... are an A.P. such that a1 + a5 + a10 + a15 + a20 + a24 = 225, then a1 + a2 + a3 + ...... + a23 + a24 is equal to ______.
