Comprehension
Your elder brother wants to buy a car and plans to take a loan from a bank for his car. He repays his total loan of 1,18,000 by paying every month, starting with the first instalment of1,000 and he increases the instalment by 100 every month.
Question: 1

Find the amount paid by him in the \( 30^{\text{th}} \) instalment.

Show Hint

Always identify 'a' and 'd' correctly from the word problem. The "starting amount" is 'a' and the "monthly increase" is 'd'.
Updated On: Feb 23, 2026
Show Solution

Solution and Explanation

Step 1: Understanding the Concept:
The monthly instalments increase by a fixed amount every month.
Therefore, they form an Arithmetic Progression (A.P.).

Step 2: Given Information:
First term (a) = 1000
Common difference (d) = 100
Required term number (n) = 30

Step 3: Using the nth Term Formula:
an = a + (n − 1)d

Substitute the values:
a30 = 1000 + (30 − 1) × 100
= 1000 + 29 × 100
= 1000 + 2900
= 3900

Final Answer:
The amount paid in the 30th instalment is Rs 3,900.
Was this answer helpful?
0
Question: 2

If the total number of instalments is 40, what is the amount paid in the last instalment ?

Show Hint

The "last instalment" is simply the term corresponding to the total number of periods given in the problem.
Updated On: Feb 23, 2026
Show Solution

Solution and Explanation

Step 1: Understanding the Concept:
The instalments form an Arithmetic Progression (A.P.).
The last instalment means the 40th term of the A.P.

Step 2: Given Information:
First term (a) = 1000
Common difference (d) = 100
Term number (n) = 40

Step 3: Using the Formula for nth Term:
an = a + (n − 1)d

a40 = 1000 + (40 − 1) × 100
= 1000 + 39 × 100
= 1000 + 3900
= 4900

Final Answer:
The amount paid in the last (40th) instalment is Rs 4,900.
Was this answer helpful?
0
Question: 3

What amount does he still have to pay after the \( 30^{\text{th}} \) instalment ?

Show Hint

When asked for "remaining amount", always calculate the sum paid so far using the \( S_n \) formula, not just the \( n^{\text{th}} \) term.
Updated On: Feb 23, 2026
Show Solution

Solution and Explanation

Step 1: Understanding the Concept:
The instalments form an Arithmetic Progression (A.P.).
To find the remaining amount after 30 instalments, we first calculate the sum of the first 30 instalments and subtract it from the total loan amount.

Step 2: Given Information:
First instalment (a) = 1000
Common difference (d) = 100
Number of instalments paid (n) = 30
Total loan amount = Rs 1,18,000

Step 3: Using the A.P. Sum Formula:
Sum of first n terms:
Sn = n/2 [2a + (n − 1)d]

S30 = 30/2 [2(1000) + (30 − 1) × 100]
= 15 [2000 + 2900]
= 15 × 4900
= 73,500

Step 4: Calculating Remaining Amount:
Remaining amount = Total loan − S30
= 1,18,000 − 73,500
= 44,500

Final Answer:
The amount left to pay after the 30th instalment is Rs 44,500.
Was this answer helpful?
0
Question: 4

Find the ratio of the tenth instalment to the last instalment.

Show Hint

Always simplify the ratio by canceling out common factors (like zeros) to reach the simplest integer form.
Updated On: Feb 23, 2026
Show Solution

Solution and Explanation

Step 1: Understanding the Concept:
A ratio is the comparison of two quantities through division. In this problem, we need to find the values of the \( 10^{\text{th}} \) and \( 40^{\text{th}} \) instalments, then compute their ratio.

Step 2: Step-by-Step Calculation:
To find the \( 10^{\text{th}} \) instalment (\( a_{10} \)):
\[ a_{10} = 1000 + (10 - 1) \times 100 = 1000 + 900 = 1900 \] To find the \( 40^{\text{th}} \) instalment (\( a_{40} \)):
From part (ii), \( a_{40} = 4900 \).
Now, calculate the ratio \( a_{10} : a_{40} \):
\[ \text{Ratio} = \frac{1900}{4900} = \frac{19}{49} \] Step 3: Final Answer:
Therefore, the ratio is 19 : 49.
Was this answer helpful?
0

Top Questions on Arithmetic Progression

Questions Asked in CBSE Class X exam