After dividing an amount into two parts, Mr. Suresh invests these parts in two different business.

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20 Aug 2009 profit and loss

After dividing an amount into two parts, Mr. Suresh invests these parts in two different business.
In first, he gains 50% profit whereas in second he has a loss of 25 %.Total profit of
Mr. Suresh in first business is 1888 rupee. What is the total investment of Mr. Suresh if he gains
23 % profit over all.

OPtion

1. 5775
2. 6465
3. 5900
4. 6732
5. 6963
6. 5421
7. 5328
8. 5855
9. 5515
10. 6712

Solution

(One variable solution)
Consider that 100 Rs is invested, then two parts are x & (100 - x)
Taking 50 % profit x becomes (3/2) x
& taking 25% loss (100 – x) becomes (3/4)(100 – x)
As total profit is 23 % hence
[(3/2)x +(3/4)(100 – x)] – 100 = 23
On solving x = 64
Profit = 64 * 50/100 = 32 in every 100 rupee
Overall profit in first business = 1888
Total investment = 100 * 1888 / 32 = 5900

Alternate method
Let total investment = P & part investments are x & (P – x)
According to given condition
x/2 = 1888 implies x = 3776
Similarly according to other condition
3x/2 +(3/4)(P – x) = P 123/100
=>3/2 * 3776 +(3/4)(P – 3776) = P 123/ 100
=>3 * 1888 + (3 /4) P – 3 * 944 = 123 P/100
=>5664 – 2832 = 123 P /100 – (3/4) P
=>2832 = (123 P – 75 P)/100
=>2832 = 48 P/100
=>P = 2832 * 100/ 48 = 5900.

Correct Option: 3 Best Solution (2)

Deepak   15 years AGO

Lets the parts be P=x+y,
(x+y)*23/100=profit of first business-loss of second business,
(x+y)*23/100=1888-y/4,as x/2=1888,
which gives y=2124 Rs and x=3776 so total investment=x+y=5900 Rs

Like? Yes (2) | No   

ashwin   15 years AGO

Let investments be x & y
50% profit is 1888..so x is 3776
(1888+25% of y)/(x+y)=23%
Substitute x and solve for y.. y=2124
x+y=5900 ie total investment

Like? Yes (1) | No