Question

A sum when lent at the rate of 15% p.a. simple interest for x years amounted to INR 17,600. When

the same sum was lent at the rate of 18% p.a. simple interest for (x+2.5) years, it amounted to INR 24,320.

The value of x and the sum (in INR) respectively are:

A. 2.5 and 12,800

B. 2 and 12,500

C. 3.5 and 12,800

D. 2.5 and 12,500​

Answer 1

Answer:

12

Step-by-step explanation:

Amount in 5 years = (principal SI for 5 years) =Rs4160.

Amount in 2 years = (principal SI for 2 years) = 3224.

On subtracting we get :

SI for 3 years = Rs(4160−3224) = Rs936.

Or SI for 2 years = Rs(936x2/3) = Rs624.

Or sum = (amount for 2 years) - (SI for 2 years) = Rs(3224−624) = Rs2600.

Now, principal = 2600, SI=Rs624, time=2years.

Therefore, rate =(100xSI)/(PxT)= (100x624)/(2600x2)% =12%p.a.

Answer 2

The value of x and the sum (in INR) respectively are: A. 2.5 and 12,800

Given - Amount, rate and time

Find - Value of x and sum

Solution - The main formula to be used in the calculation is -

S.I. = $\frac{P × R × T}{100}$

In this formula, S.I. is simple interest, P is principal, T is time and R is rate of interest.

Also, another relation to be used for solving is -

Amount = Principal + Interest

Interest = Amount - Principal

For the first case -

$17600 - P = \frac{P \times 15 \times x}{100}$

Solving the mentioned equation to find the equation -

1760000 - 100P = 15Px - Equation 1

For the second case -

$24320 - P = \frac{P \times 18 \times (x + 2.5)}{100}$

2432000 - 100P = 18Px + 45P

2432000 - 145P = 18Px - Equation 2

Dividing equation 1 by 5

352000 - 20P = 3Px - Equation 3

Multiplying equation 3 with 6

2112000 - 120P = 18Px - Equation 4

Subtracting Equation 4 from Equation 2

2432000 - 145P = 18Px

2112000 - 120P = 18Px

We get -

32000 - 25P = 0

25P = 320000

P = $\frac{320000}{25}$

P = 12,800

Keep value of P in Equation 1 to find the value of x

1760000 - 100×12800 = 15×12800×x

1760000 - 1280000 = 192000x

480000 = 192000x

$x = \frac{480000}{192000}$

x = 2.5

Hence, value of x is 2.5 and sum is Rs. 12,800.

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