Shreya and Supriya enter into a partnership deal with the investment of Rs. 6000 and Rs. 4000 respectively. After the end of the 5 months, Prerna joins them with an investment of Rs.2,000. If Supriya withdraws her capital after 4 months, how would they share a profit of Rs. 24800 at the end of 7 months?

Solution

It is clear from the question that Shreya invested Rs.6,000 for 7 months, Supriya invested Rs. 4,000 for 4 months and Prerna invested Rs. 2,000 for 2 months. So,the ratio of their investments (Shreya’s : Supriya’s : Prerna’s)= 6,000 × 7 : 4,000 × 4 : 2,000 × 2 = 42,000 : 16,000 : 4,000 = 21 : 8 : 2 Let shares of Shreya, Supriya and Prerna be 21x [if gte msEquation 12]> x [if !msEquation]-->[endif]-->, 8x [if gte msEquation 12]>x [if !msEquation]-->[endif]--> and 2x [if gte msEquation 12]>x [if !msEquation]-->[endif]-->. [if gte msEquation 12]>∴ [if !msEquation]-->[endif]-->21x [if gte msEquation 12]> x [if !msEquation]-->[endif]-->+ 8x [if gte msEquation 12]>x [if !msEquation]-->[endif]-->+ 2x [if gte msEquation 12]>x [if !msEquation]-->[endif]--> = 24,800 ⇒ 31x = 24,800 [if gte msEquation 12]>∴ x [if !msEquation]-->[endif]-->=> x = 800 [if gte msEquation 12]>∴ [if !msEquation]-->[endif]-->Shreya’s share in profit = 21 x 800 = Rs. 16,800 Supriya’s share in profit = 8 x 800 = Rs. 6,400 Prerna’s share in profit = 2 x 800 = Rs. 1,6 00
Method II: Shreya investment for 7 months = 6,000 × 7= 42,000 Supriya investment for 4 months = 4,000 × 4 = 16,000 Prerna investment for 2 months = 2,000 × 2= 4,000 Shreya: Supriya:Prerna= 21 : 8 : 2 Shraya’s share = `(21/31) x 24800` = Rs. 16,800 Supriya’s share = `(8/31) x 24800` = Rs. 6,400 Prerna’s share = `(2/31) x 24800` = Rs. 1,6 00