Question

A telephone service provider charges a price of P for a new connection, and allows 30 tree calls within that. On every extra call beyond the 30th one, the charge is Rs 5. Raja has 2 connections, on one of which he makes Q calls, and on the other, R calls, (where both Q and R are greater than or equal to 30) resulting in 2 bills of Rs 500 and Rs 400 respectively. Had he made all the calls on a single connection instead, his bili
would have come to just Rs 800.
1) What is the value of P?
1) Rs 150
2) Rs 200
3) Rs 250
4) Rs 300

2) What is the value of Q?
1) 30
2) 50
3) 60
4) 80

3) What is the value of R?
1) 30
2) 50
3) 60
4) 80


And please mention steps as well with the answers....​

Answer 1

1) value of P is 250 Rs

2)value of Q is 80 Rs

3) value of R is 60 Rs

•Case 1 : When Raja makes Q calls

•For 30 calls charges are P Rs

for rest of calls i.e. (Q-30) calls charges are 5 Rs per call

so, P + 5(Q-30) = 500

• P + 5Q = 650 _____(1)

•Case 2 : When Raja makes R calls

•For 30 calls charges are P Rs

for rest of calls i.e. (R-30) calls charges are 5 Rs per call

so, P + 5(R-30) = 400

•P + 5R = 550 _____(2)

•Case 3 : When Raja makes Q+R calls

•For 30 calls charges are P Rs

for rest of calls i.e. (Q+R-30) calls charges are 5 Rs per call

so, P + 5(Q+R-30) = 500

• P + 5(Q+R) = 950 _____(3)

•Now , subtracting (2) from (1)

5(Q-R) = 100

(Q-R) = 20

•Q = R + 20 ______(4)

•Putting (4) in (3)

P + 5(R+20+R) = 950

P + 5(2R +20) = 950

•P + 10R = 850 ______(5)

•Multiplying (2) by 2

2P + 10R = 1100 _______(6)

•Subtracting (5) from (6)

P = 250

•Now putting P = 250 in (6)

2(250) + 10R = 1100

500 + 10R = 1100

10R = 600

•R = 60 ______(7)

•Putting (7) in (4)

Q = (60) + 20

•Q = 80