Question

Two traders $X$ and $Y$ buy goods from one another, each allowing the other one months credit.
At the end of $3$ months the accounts rendered are as follows :

	Gold sold by $X$ to $Y$ (in Rs)		Gold sold by $Y$ to $X$ (in Rs)
April $18$	$60.00$	April $23$	$52.00$
May $15$	$70.00$	May $24$	$50.00$
June $16$	$80.00$

Calculate the date upon which the balance should be paid so that no interest is due either to $X$ or $Y$.

• A. May $18$
• B. June $29$
• C. May $30$
• D. June $30$

Answer 1

Answer: (B)

June $29$

Taking May ${18}^{th}$ as the base date.

For $Y^{\prime }s$ payments:

Date of Transaction	Due Date	Amount	No. of days from the base date	Products
April 18	May 18	60	0	0
May 15	June 15	70	28	1960
June 16	July 16	80	59	4720
Amount Due to $X$		$210$	Sum of products	$6680$

$\Rightarrow$ For $X^{\prime }s$ payments.

$\Rightarrow$ Here, also we are taking same base date.

Date of Transaction	Due Date	Amount	No. of days from the base date	Products
April 23	May 23	52	5	260
May 24	June 24	50	37	1850
Amount Due to $Y$		$102$	Total products	$2110$

Excess of $Y^{\prime }s$ products over $X^{\prime }s$ $=$ $6680-2210=4570.$

Excess amount due to $X$ $=$ Rs. $210-$ Rs. $102=$ Rs. $108$.

Number of days from the base date to the date of settlements $=$ $\frac{4570}{108}=42$ days

The date of settlement of balance is $42$ days after May $18$ i.e. on June $29.$

On June $29$, $Y$ has to pay $X$, Rs. $108$ to clear the account.