A sum of ₹1200 becomes ₹1560 at the rate of simple interest in 3 years. In how many years will the sum of ₹800 amounts to ₹1120 at the same rate of simple interest?

Correct option is C

Given:
Principal P=₹1200 
Amount after 3 years = ₹1560
Formula Used:
Simple Interest = $$\frac{P \times R \times T}{100}$$​​

where P is the principal, R is the rate of interest, and T is the time in years.

Amount = Principal + Simple Interest​​
Solution:
Amount = Principal + Simple Interest
​$$1560 = 1200 + \frac{1200 \times R \times 3}{100}$$​​

​$$1560 - 1200 = \frac{1200 \times R \times 3}{100}$$​

​$$360 = \frac{3600R}{100}$$​​

360 = 36R

R = $$\frac{360}{36} = 10\%$$​​

So, the rate of interest is 10% per annum.
Now, calculating the time for ₹800 to amount to ₹1120:
Amount = Principal + Simple Interest

​$$1120 = 800 + \frac{800 \times 10 \times T}{100}$$​

​$$1120 - 800 = \frac{800 \times 10 \times T}{100}$$​​

​$$320 = \frac{8000T}{100}$$​​
320 = 80T
$$T = \frac{320}{80} = 4 \,$$​ years
The sum of ₹800 will amount to ₹1120 in 4 years.

Thus, the correct option is (c) 4 years

Alternate Method:

Principal : Amount

1200       :  1560

SI in 3 years = 360

Si in 1 year = $$\frac{360}{3} = 120$$

SI = 120 , T = 1, P = 1200

Rate = $$\frac{120}{1200} \times \frac{100}{1}$$ = 10%

Principal : Amount

800         :  1120

SI = 320

Time = $$\frac{320}{800} \times \frac{100}{10}$$ = 4 years​

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