## Problems on percentage

Aptitude Solved Problems
Questions :

1. A man purchased a bicycle for Rs. 4800 and sold it immediately at Rs. 5995, allowing the buyer a credit of one and a half years. If the rate of interest is 6%, then find the man gains ?

2. A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:

3. Raja and Ravi invest in a business in the ratio 3 : 2. Assume that 5% of the total profit goes to charity. If Raja share is Rs. 855, what is the total profit?

1. Explanation:

Amount = Rs. 4800
Selling price ( Present Worth of Rs. 5995 due 1.5 years ) = ( Amount * 100 ) / ( 100 + ( Rate * Time ))
= ( 5995 * 100 ) / ( 100 + ( 6 * 1.5 ))
= ( 5995 * 100 ) / ( 100 + 9 )
= ( 5995 * 100 ) / 109
= ( 55 * 100 )
= 5500
Gain = Selling Price – Cost price
= ( 5500 – 4800 )
= Rs. 700
∴ Gain of the man is Rs. 700.

2. Explanation:

Selling price = Present Worth Rs. 2200 due 1 year.
Present Worth = Rs. 2200
Time = 1 year
Rate of interest = 10%
Present Worth = ( 100 * Amount ) / 100 + ( Rate * Time )
= ( 2200 * 100 ) / 100 + ( 10 * 1 )
= Rs. 2000
Gain = ( Selling Price – Cost price )
Gain = Rs. (2000 – 1950)
= Rs. 50
∴ His Gain is Rs. 50.

3. Explanation:

Assume that the total profit is x
Since 5% goes for charity,
95% of x will be divided between Raja and Ravi in the ratio 3 : 2
Therefore, Raja profit
= ( 95x / 100 ) * 3 / 5
Given that Raja share is Rs. 855. Therefore,
( 95x / 100 ) * ( 3 / 5 ) = 855
( 95x / 100 ) = 855 * ( 5 / 3 )
( 95x / 100 ) = ( 285 * 5 )
x = 1425
x = ( 1425 * 100 ) / 95
= ( 285 * 100 ) / 19
= 1500
∴ Hence the total profit is Rs. 1500.