Question
Find the values of x, y and z, so as to satisfy the
equations given below: x + y + z = 12; x + y – z = 6; x – y + z = 4Solution
We are given: x + y + z = 12 x + y − z = 6 x − y + z = 4 Add (1) and (2): (x + y + z) + (x + y − z) = 12 + 6 ⇒ 2x + 2 y = 18 ⇒ x + y = 9 Subtract (2) from (1): (x + y + z) − (x + y − z) = 12 − 6 ⇒ 2z = 6 ⇒ z = 3 Substitute z = 3 into (3): x − y + 3 = 4 ⇒ x − y = 1 Now, solve: x + y = 9 x − y = 1 Add both: 2x = 10 ⇒ x = 5 Then, y = 4
A invests Rs. 20,000 for 6 months, B invests Rs. 15,000 for 8 months, C invests Rs. 25,000 for 4 months. Total profit = Rs. 17,000. Find B’s share.
Ashu and Sunil together start a business with investment of Rs. 1800 and Rs. ‘x + 1000’, respectively. If the profit earned after 5 years is Rs. 640...
'A' and 'B' invested Rs. 16,000 and Rs. 12,000, respectively, in a business. After 8 months, 'A' added Rs. 8,000 to his investment, while 'B' withdrew R...
Deepak and Ramesh started a business by investing Rs. ‘X’ and Rs. (X + 600), respectively. 12 months later, Ramesh withdrew his entire investment. ...
‘A’ and ‘B’ started a business by investing certain sum in the ratio 3:2, respectively for 10 years. If 20% of the total profit is donated in an...
"Abhinav" and "Pankaj" launched a business venture with investments of Rs. 1400 and Rs. 2100, respectively. The ratio of the time for which "Abhinav" an...
Ashish started a business by investing Rs. 6300. Few months later; Ramesh joined him by investing Rs. 8000 such that at the end of the year, the profit ...
A and B started a retail store with initial investments in the ratio 5:6 and their annual profits were in the ratio 2:3. If A invested the money for 8 m...
X started a business with Rs.12000. After 6 months, Y joined with x% of X’s capital. At the end of the year, Y’s share in the Rs.36000 total profit ...
- Ravi and Raj entered into a business where Ravi invested Rs. 9,000. Raj withdrew his capital after 6 months. If their profit ratio at the end of the year w...
Relevant for Exams:
