# A boy presented a cheque at his bank. The teller intended to give him in notes of 2 denominations,Rs. 50 and Rs.500. He planned to give him 'x' number of Rs.50 notes and 'y' no. of Rs.500 notes....

A boy presented a cheque at his bank. The teller intended to give him in notes of 2 denominations,Rs. 50 and Rs.500.

He planned to give him 'x' number of Rs.50 notes and 'y' no. of Rs.500 notes. But while paying, the teller was distracted and he gave him 'y' Rs.50 notes and 'x' Rs.500 notes.

Boy pocketed the cash without verifying.He had no money other than what teller gave him. After spending Rs.350,he found that he had double the amount for which he had presented the cheque.If the amount of the cheque was Rs.P, which of the following could be true?

a) 1000< P <1500

b) 1500< P <2000

c) 2000< P <2500

d) 2500< P <3000

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Cheque amount: 50x + 500y = P --- (1)

The amount paid by teller = 500x + 50y

Amount left after spending Rs.350 = 500x + 50y - 350, which is double the cheque amount

therefore 500x + 50y - 350 = 2(50x+500y)

500x+50y-350 = 100x+1000y

=> 400x-950y = 350 --- (2)

multiplying (1) by 4 and (2) by 5, we get:

2000x+200y = 4P ---- (3)

2000x-4750y= 1750 (4)

subtracting (4) from (3), we get:

4950y = 4P-1750

=> y = (4P-1750)/4950 --- (5)

or y>0 only if 4P>1750 or P>437.5

and substituting the value of y in (1) we get:

50x+500(4P-1750)/4950 = P

=> x = P - 500(4P-1750)/4950

=> x = (2950P-875000)/4950 --- (6)

substituting the values of x and y from (5) and (6) in 3 we get:

400(2950P-875000)/4950+950(4P-1750)/4950=350

solving above for P, **we get P = 2975.74**

As P is equal to 2975.74, therefore option d is true and the answer is:

**d) 2500 < P < 3000 is true**