Advertisements
Advertisements
Question
A merchant borrows ₹ 1000 and agrees to repay its interest ₹ 140 with principal in 12 monthly instalments. Each instalment being less than the preceding one by ₹ 10. Find the amount of the first instalment.
Advertisements
Solution
The installments are in A.P.
Amount repaid in 12 instalments (S12)
= Amount borrowed + Total interest
= 1000 + 140
∴ S12 = 1140
Number of instalments (n) = 12
Each instalment is less than the preceding one by ₹ 10.
∴ d = –10
Now, `S_n = n/2 [2a + (n - 1)d]`
∴ `S_12 = 12/2 [2a + (12 - 1)(-10)]`
∴ 1140 = 6[2a + 11(– 10)]
∴ 1140 = 6(2a – 110)
∴ `1140/6` = 2a – 110
∴ 190 = 2a – 110
∴ 2a = 300
∴ a = `300/2`
∴ a = 150
∴ The amount of first instalment is ₹ 150.
RELATED QUESTIONS
Three numbers are in A.P. If the sum of these numbers is 27 and the product 648, find the numbers.
Find the sum of n terms of an A.P. whose nth terms is given by an = 5 − 6n.
Find the sum of first 22 terms of an A.P. in which d = 22 and a = 149.
Find the sum of all integers between 100 and 550, which are divisible by 9.
In an A.P., if the 5th and 12th terms are 30 and 65 respectively, what is the sum of first 20 terms?
Find the sum 2 + 4 + 6 ... + 200
Find the sum:
25 + 28 + 31 + ... + 100
Which term of AP 72, 68, 64, 60, ... is 0?
The 7th term of an AP is –4 and its 13th term is –16. Find the AP.
How many three-digit natural numbers are divisible by 9?
The first term of an AP is p and its common difference is q. Find its 10th term.
How many terms of the AP `20, 19 1/3 , 18 2/3, ...` must be taken so that their sum is 300? Explain the double answer.
Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and times the corresponding sides of ΔPQR?
Choose the correct alternative answer for the following question.
For an given A.P. a = 3.5, d = 0, n = 101, then tn = ....
The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28th term of this A.P.
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
The first three terms of an A.P. respectively are 3y − 1, 3y + 5 and 5y + 1. Then, y equals
Q.18
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.
The 5th term and the 9th term of an Arithmetic Progression are 4 and – 12 respectively.
Find:
- the first term
- common difference
- sum of 16 terms of the AP.
