Time and Work
- A can do a piece of work in 16 days and B in 24 days. They take the help of C and three together finish the work in 6 days. If the total remuneration for the work is ₹ 400. The amount (in rupees)each will receive, in proportion, to do the work is
-
View Hint View Answer Discuss in Forum
Rule 3 and Rule 25,
If C alone completes the work in x days, then= 1 + 1 + 1 = 1 16 24 x 6 ⇒ 1 = 1 - 1 - 1 x 6 16 24 = 8 - 3 - 2 = 1 48 16
⇒ x = 16 days
∴ Ratio of their remuneration= 1 : 1 : 1 = 3 : 2 : 3 16 24 16
∴ A’s remuneration= 3 × 400 = ₹ 150 8
B’s remuneration= 2 × 400 = ₹ 100 8
C’s remuneration= 3 × 400 = ₹ 150 8
⇒ A : 150, B : 100, C : 150Correct Option: A
Rule 3 and Rule 25,
If C alone completes the work in x days, then= 1 + 1 + 1 = 1 16 24 x 6 ⇒ 1 = 1 - 1 - 1 x 6 16 24 = 8 - 3 - 2 = 1 48 16
⇒ x = 16 days
∴ Ratio of their remuneration= 1 : 1 : 1 = 3 : 2 : 3 16 24 16
∴ A’s remuneration= 3 × 400 = ₹ 150 8
B’s remuneration= 2 × 400 = ₹ 100 8
C’s remuneration= 3 × 400 = ₹ 150 8
⇒ A : 150, B : 100, C : 150
- If the expenditure of gas on burning 6 burners for 6 hours a day for 8 days is 450, then how many burners can be used for 10 days at 5 hours a day for 625 ?
-
View Hint View Answer Discuss in Forum
Using Rule 1,
Tricky Approach
∴ 450 : 625 
: : 6 : x 10 : 8 5 : 6
⇒ 450 × 10 × 5 × x
= 625 × 8 × 6 × 6⇒ x = 625 × 8 × 6 × 6 = 8 450 × 10 × 5 Correct Option: D
Using Rule 1,
Tricky Approach∴ 450 : 625 : : 6 : x 10 : 8 5 : 6
⇒ 450 × 10 × 5 × x
= 625 × 8 × 6 × 6⇒ x = 625 × 8 × 6 × 6 = 8 450 × 10 × 5
- A can do a piece of work in 60 days. He works for 15 days and then B alone finishes the remaining work in 30 days. The two together can finish the work in
-
View Hint View Answer Discuss in Forum
Work done by A in 15 days
= 1 × 15 = 1 60 4
Remaining work= 
1 - 1 
= 3 4 4
Now, 3/4 work is done by B in 30 days
Whole work will be done by B in= 30 × 4 = 40 days 3 A’s 1 day’s work = 1 and B’s 1 day’s work 60 = 1 40
(A + B)’s 1 day’s work= 1 + 1 = 2 + 3 = 1 60 40 120 24
Hence, both will finish the work in 24 daysCorrect Option: A
Work done by A in 15 days
= 1 × 15 = 1 60 4
Remaining work= 1 - 1 = 3 4 4
Now, 3/4 work is done by B in 30 days
Whole work will be done by B in= 30 × 4 = 40 days 3 A’s 1 day’s work = 1 and B’s 1 day’s work 60 = 1 40
(A + B)’s 1 day’s work= 1 + 1 = 2 + 3 = 1 60 40 120 24
Hence, both will finish the work in 24 days
- A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do the work in
-
View Hint View Answer Discuss in Forum
A’s 1 day’s work = (B +C)’s 1 day’s work ...(i)
(A + B)’s 1 day’s work = 1 10 C’s 1 day’s work = 1 50
(A + B + C)’s 1 day’s work= 1 + 1 = 5 + 1 = 3 ...............(iii) 10 50 50 25 (A + A)’s 1 day’s work = 3 25
(By (i) & (iii)A’s 1 day’s work = 3 50
B’s 1 day’s work= 1 - 3 10 50 = 5 - 3 = 2 = 1 50 50 25
Hence, B alone will complete the work in 25 days.Correct Option: C
A’s 1 day’s work = (B +C)’s 1 day’s work ...(i)
(A + B)’s 1 day’s work = 1 10 C’s 1 day’s work = 1 50
(A + B + C)’s 1 day’s work= 1 + 1 = 5 + 1 = 3 ...............(iii) 10 50 50 25 (A + A)’s 1 day’s work = 3 25
(By (i) & (iii)A’s 1 day’s work = 3 50
B’s 1 day’s work= 1 - 3 10 50 = 5 - 3 = 2 = 1 50 50 25
Hence, B alone will complete the work in 25 days.
- A man can do a piece of work in 5 days, but with the help of his son, he can do it in 3 days. In what time can the son do it alone ?
-
View Hint View Answer Discuss in Forum
Using Rule 2,
Let the son take x days to do the work.∴ 1 + 1 = 1 5 x 3 ⇒ x + 5 = 1 5x 3
⇒ 3x + 15 = 5x⇒ 2x = 15 ⇒ x= 15 2 7 1 days 2 Correct Option: C
Using Rule 2,
Let the son take x days to do the work.∴ 1 + 1 = 1 5 x 3 ⇒ x + 5 = 1 5x 3
⇒ 3x + 15 = 5x⇒ 2x = 15 ⇒ x= 15 2 7 1 days 2
