Rs.3500 has been divided between three
persons P, Q and R in such a way that if their
shares are diminished by Rs.30, Rs.40 and
Rs.50 respectively, the remainders are in
the ratio 7:4:9. Find the share of Q
Answers
Step-by-step explanation:
Given Rs.3500 has been divided between three persons P, Q and R in such a way that if their shares are diminished by Rs.30, Rs.40 and
Rs.50 respectively, the remainders are in the ratio 7:4:9. Find the share of Q
- Total amount distributed among P,Q and R = Rs 3500
- Total amount diminished is Rs (30 + 40 + 50) = Rs 120
- Rest of the amount will be Rs (3500 – 120) = Rs 3,380
- We need to divide Rs 3,380 in the ratio 7:4:9
- Therefore P’share will be Rs 7 / 7 + 4 + 9 x 3,380
- = 7 / 20 x 3,380
- = 1,183 + 7
- =Rs 1,190
- Q share will be Rs 4 / 20 x 3,380
- = 676 + 4
- = Rs 680
Answer:
The share for Q is rs 716
Step-by-step explanation:
Let p and q be the shares of P and Q respectively.
The share of R is given by:
R = 3500 - (p + q)
R = 3500 - p - q
Their shares are reduced by rs 30, 40, and 50 respectively.
So, we have:
P = p - 30
Q = q - 40
R = 3500 - p - q - 50 = 3450 - p - q
The ratio of these amounts is 7:4:9
P : Q = 7:4 = (p - 30)/(q - 40)
7(q - 40) = 4(p - 30)
7q - 280 = 4p - 120
7q - 4p = 160
The ratio of Q to R is = 4:9
4/9 = (q - 40)/(3450 - p - q)
4(3450 - p - q) = 9(q - 40)
13800 - 4p - 4q = 9q - 360
14160 = 4p + 13q
We have two simultaneous equations as follows:
7q - 4p = 160............1
4p + 13q = 14160................2
Let'a add the two equations to eliminate p as follows:
20q = 14320
q = 716
Substituting in 1 we have:
7 × 716 - 4p = 160
-4p = -5012 + 160
p = 1213
The share for R = 3500 - (1213 + 716) = 1571
The share of Q is Rs 716