9. P can do a piece of work in x days. He finished 1/6th of the whole work and then Q alone did the rest of the work in 15 days. If together they can finish half of the whole work in 45/8 days, then find the value of x?
P can do a work in X days. He finished 1/6 of the entire work and then Q alone finished the rest in 15 days. If together they can finish half of the work in 45/8 days, then find the value of
X? (RRB NTPC 2016)
(a) 90/11
(c) 42
(b) 30
(d) 32/8
UPSI 14 BOOKS COMBO EXAMPUR through OFFICIAL APP NOW 9873111552
Answers
Answer:
a) 90/11
Step-by-step explanation:
take total units of work as 900 units.
if they take 45/8 days.. then each day they do 900/(45/8) = 160 units of work.
q alone did 5/6 (900) units in 15 days.. so per day he did 750/15 = 50 units of work.
so p did 160-50= 110 units of work.
therefor. x = 900/110 = 90/11
Given:
P finished (1/6) part of the work in X days.
Q alone finished the remaining work in 15 days
They can finish half work together in 45/8 days
Concept used:
If A does 1 unit of work in n day
Then 1 day work done by A will be 1/n units
1/(A’s work) + 1/(B’s work) = 1/(total work together)
Calculation:
Time to complete the whole wok by P alone = X days
P complete (1/6) work
Remaining work = 1 – (1/6) = 5/6
Q complete (5/6) work in 15 day
Q complete work = 15/(5/6)
Q complete work = 18 days
(P + Q)’s half work complete in 45/8 days
(P + Q)’s complete work [(45/8) × 2] = 45/4 days
So,
(1/P’s work) + (1/Q’s work) = [1/(P + Q)’s work}
⇒ (1/X) + (1/18) = 1/(45/4)
⇒ 1/X = (4/45) – (1/18)
⇒ 1/X = (8 – 5)/90
⇒ 1/X = 3/90
⇒ 1/X = 1/30
⇒ X = 30
∴The value of X is 30.
Formula Used:
Total work = Efficiency × Days required to complete the work
M1.D1.T1.E1/W1.C1 = M2.D2.T2.E2/W2.C2
M is the number of working men
D is the total number of days
T is total hours of working days
E is the efficiency of working men
W is total work
C is the consumption of working men
Calculation:
(P + Q) completed 1/2 work in 45/8 days
Total work will get complete in = 45/8 × 2 = 45/4 days
P completes 1/6 work in X days.
Remaining work = 1 - 1/6 = 5/6 completed by Q in 15 days.
Now by using the formula,
⇒ (Q × 15)/5/6 = {(P + Q) × 45/4}/1
⇒ 4 × (18 × Q) = 45(P + Q)
⇒ 72 Q = 45(P + Q)
⇒ 8Q = 5(P + Q)
⇒ 3Q = 5P
Efficiency of P is 3 units/day
Efficiency of Q is 5 units/day
(P + Q) completed work in 45/4 days
⇒ Total work = 45/4 × (3 + 5) = 45/4 × 8 = 90 units
Days required to complete 90 units of work by P is,
⇒ Days = 90/3 = 30 days
∴ Time required to complete the work by P is 30 days.
I HOPE THIS HELPS YOU.
AND PLEASE MARK ME AS BRAINLIEST.
♥️♥️