2 2 9 8 4 7

# TIME & WORK SET 4

Q.1 Two workers A & B working together completed a job in 5 days. If A worked twice as efficiently as he actually did & B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require ?

A) 7 ½ days

B) 6 ¼ days

C) 8 ¾ days

D) 5 1/5 days

Ans. B

Let A & B completes the job in x & y days
Thus, 1/x + 1/y = 1/5–i
After changing efficiencies A would be able to complete the work in x/2 days & B in 3x days
Therefore, 2/x + 1/3y = 1/3—ii
On solving these two equations we will get
X = 6 ¼ days

Q.2 A & B can complete a job in 24 days. A alone can complete in 32 days. Both of them worked together for 8 days & then A left. The number of days B will take to complete the remaining job is :

A) 32 days

B) 128 days

C) 64 days

D) 16 days

Ans. C

1/A + 1/B = 1/24 & 1/A = 1/32
1/B = 1/24-1/32= 1/96
B = 96 days
Now, 8/32 +8+x / 96 = 1
Or 24+8+x=96
X=96-32= 64

Shortcut:
vab
i.e. v 16 * 9 = 12 days

Q.3 Ashok started a business with an investment of Rs. 10000. After a few months Alok joined him with an investment of Rs. 12000. At the end of one year from the start they shared Alok total profit equally. After how long did join ?
A) 2 months
B) 3 months
C) 4 months
D) 5 months
Ans. A
10000 * 12 / 12000 * x = 1:1
10 / x = 1:1
X=10
Therefore , he joined the business with Ashok after 2 months

Q.4 X & Y started a business with an investment of Rs.20000 & Rs.24000. At the end of one year total profit they shared was Rs.1000 more than the difference in their profit shares. Find the total profit ?
A) 1100
B) 1200
C) 1300
D) 1400
Ans. A
20000 : 24000 = 5 : 6
Let the total profit share be 5x & 6x
5x + 6x = 6x – 5x + 1000
Therefore, 11x = x+1000
X=100
Therefore, total profit = 6x+5x = 11x
Or 11 * 100 = 1100

Q.5 A & B enter into the specification A puts in Rs. 50 & B puts in Rs. 45. At the end of 4 months A withdrew half his capital & at the end of 6 months B withdraw half of its capital. C then enters with a capital of Rs. 70. At the end of 12 Months in what ratio will the profit be divided ?
A) 80 : 81 : 84
B) 82 : 83 : 85
C) 86 : 88 : 89
D) 91 : 93 : 95
Ans. A
A = 50 * 4 + 50/2 * 8 : 45*6 + 45/2*6 : 70*6
Or 400 :405:450
=80:81:84