Question

Rs. 12000 is divided into 2 parts such that the simple interest on the first part for 3 years at 12% per annum may be equal to the simple interest on the second part for 4.5 years at 16% per annum. The ratio of the first part to the second part is ?

Answer 1

Given :

Rs. 12000 is divided into 2 parts such that the simple interest on the first part for 3 years at 12% per annum may be equal to the simple interest on the second part for 4.5 years at 16% per annum.

• To find : The ratio of the first part to the second part

Solution :

Rs. 12000 is divided into 2 parts such that the simple interest on the first part for 3 years at 12% per annum

★ Principal (P) = 12000/2 = 6000

★ Time (T) = 3 years

★ Rate of interest (R) = 12%

→ Simple interest = P × R × T /100

→ S. I = 6000 × 12 × 3/100

→ S. I = Rs.2160

The simple interest on the second part for 4.5 years at 16% per annum.

★ Principal = 6000

★ Time = 4.5 years

★ Rate of interest = 16%

→ Simple interest = 6000 × 16 × 4.5/100

→ S. I = Rs.4320

Ratio of the first part to second part

→ Simple interest of the first part/simple interest of the second part

→ 2160/4320

→ 1 /2

→ 1 : 2

•°• Required ratio = 1:2

Answer 2

Given :-

Rs  12000 is divided into 2 parts such that the simple interest on the first part for 3 years at 12% per annum may be equal to the simple interest on the second part for 4.5 years at 16% per annum.

To Find :-

Ratio of the first part to the second part is ?

Solution :-

For first part

Since it is divide into two parts

Principal = 12000/2

Principal = 6000

SI = PRT/100

SI = 6000 × 12 × 3/100

SI = 60 × 12 × 3

SI = 2160

For second part

SI = PRT/100

SI = 6000 × 16 × 4.5/100

SI = 60 × 16 × 4.5

SI = 4320

Ratio = 2160 : 4320

Ratio = 1:2

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