Practice MCQ Questions and Answer on Time and Work

191.

Two forest officials in their respective division were involved in the harvesting of tendu leave. One division had an average output of 21 tons from a hectares and other division, which had 12 hectares of land less, dedicated to tendu leaves, got 25 tons of tendu from a hectare. As a result, the second division harvested 300 tons of tendu leaves more than the first. How many tons of tendu leaves did the first division harvest.

(A) 3150
(B) 3450
(C) 3500
(D) 3600

192.

If 16 men or 20 women can do a piece of work in 25 days. In what time will 28 men and 15 women do it ?

(A) $14 \frac{2}{7} days$
(B) $33 \frac{1}{3} days$
(C) $18 \frac{3}{4} days$
(D) $10 days$

Solution: If number of days at work is same $\begin{aligned} So, we can equate directly \\ 16 men = 20 women \\ 4 men = 5 women \\ 5 women = 4 men \\ 1 women = \frac{4}{5} men \\ 15 women = \frac{4}{5} \times 15 \\ 15 women = 12 men \end{aligned}$ ⇒ 16 men complete a work in 25 days 1 men complete a work in 400 days $\begin{aligned} 28 men + 15 women = ? \\ ↓ \\ 28 men + 12 men = 40 men \\ work in = \frac{25 \times 16}{40} \\ = 10 days \\ A l t e r n a t e : \\ 16 m or 20 w \to 25 days \\ 28 m and 15 w \to ? \\ \frac{16 \times 20 \times 25}{(16 \times 15) + (20 \times 28)} \\ = 10 days \end{aligned}$

193.

An employee pays Rs. 26 for each day a worker and forfeits Rs. 7 for each day he idle. At the end of 56 days, if the worker got Rs. 829, for how many days did the worker remain idle?

(A) 21
(B) 15
(C) 19
(D) 13

Solution: His Per day pay = Rs. 26 Total pay employee got = Rs. 829 Total pay he gets if he did not remain idle a single day, = 26 × 56 = Rs.1456 He Forfeits or fined = 1456 - 829 = Rs. 627 Per day he Forfeits Rs. 7 Means per idle day he loses = 26 + 7 = Rs. 33 So, Total idle days = $\frac{627}{33}$ = 19 days Alternatively, Let he works for X days and remain idle for (56 - X) Now, According to question, X × 26 - 7 × (56 - X) = 829 26X + 7X - 392 = 829 33X = 829 + 392 = 1221 X = 37 days Number of days remain idle = 56 -37 =19 days

194.

A and B can complete a piece of work in 12 and 18 days respectively. A begins to do the work and they work alternatively one at a time for one day each. The whole work will be completed in ?

(A) $14 \frac{1}{3} days$
(B) $15 \frac{2}{3} days$
(C) $16 \frac{1}{3} days$
(D) $18 \frac{2}{3} days$

Solution: $\begin{aligned} (A + B)'s 2 days work \\ = (\frac{1}{12} + \frac{1}{18}) \\ = \frac{5}{36} \\ Work done in 7 pairs of days \\ = (\frac{5}{36} \times 7) \\ = \frac{35}{36} \\ Remaining work \\ = (1 - \frac{35}{36}) \\ = \frac{1}{36} \\ On 15th day, it is A's turn . \\ \frac{1}{12} work is done by A in 1 day . \\ \frac{1}{36} work is done by A in \\ = (12 \times \frac{1}{36}) \\ = \frac{1}{3} day . \\ ∴ Total time taken = 14 \frac{1}{3} days \end{aligned}$

195.

A road of 5 m length will be constructed in 100 days. So, 280 workers were employed. But after 80 days it was found that only $3 \frac{1}{2}$ km road was completed. Now how many more people were need to finish the work in the specified time ?

(A) 480
(B) 80
(C) 200
(D) 100

Solution: Let 'n' more number of man are required to complete the job in 20 day. $\frac{80_{days} \times 28 0_{worker}}{3 .5 km} =$ $\frac{{(280 + n)}_{worker} \times 2 0_{days}}{1 .5 km}$ $\begin{aligned} After solving: \\ \Rightarrow 480 = 280 + n \\ \Rightarrow n = 200 \end{aligned}$

196.

P can finish a work in 18 days. When he had worked for 5 days, Q joined him. If both of them together completed the remaining work in $\frac{13}{5}$ days, then in how many days can Q alone finish $66 \frac{2}{3} %$ ÃÂÃÂ of the same work?

(A) 2
(B) 3
(C) 4
(D) 5

Solution: $\begin{aligned} Total work = 18 P = 5 P + \frac{13}{5} (P + Q) \\ 13 P = \frac{13}{5} P + \frac{13}{5} Q \\ \frac{52}{5} P = \frac{13}{5} Q \\ \frac{P}{Q} = \frac{1}{4} \\ Total work = 18 \times 1 = 18 \\ 66 \frac{2}{3} % of work = \frac{2}{3} \times 18 = 12 \\ Q days = \frac{12}{4} = 3 days \end{aligned}$

197.

A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

(A) $\frac{1}{4}$
(B) $\frac{1}{10}$
(C) $\frac{7}{15}$
(D) $\frac{8}{15}$

Solution: $\begin{aligned} A's 1 day's work = \frac{1}{15}; \\ B's 1 day's work = \frac{1}{20}; \\ (A + B)'s 1day's work \\ = \frac{1}{15} + \frac{1}{20} = \frac{7}{60} \\ (A + B)'s 4 day's work \\ = \frac{7}{60} \times 4 = \frac{7}{15} \\ ∴ Remaining work = 1 - \frac{7}{15} = \frac{8}{15} \end{aligned}$

198.

10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?

(A) 3
(B) 5
(C) 7
(D) Cannot be determined

Solution: $\begin{aligned} 1 w o m a n^{'} s 1 d a y^{'} s w o r k = \frac{1}{70} \\ 1 child's 1 day's work = \frac{1}{140} \\ (5 women + 10 children)'s day's work \\ = \frac{5}{70} + \frac{10}{140} = \frac{1}{14} + \frac{1}{14} = \frac{1}{7} \\ ∴ 5 women and 10 chidren will complete \\ the work in 7 days \end{aligned}$

199.

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

(A) Rs. 375
(B) Rs. 400
(C) Rs. 600
(D) Rs. 800

Solution: $\begin{aligned} C's 1 day's work \\ = \frac{1}{3} - (\frac{1}{6} + \frac{1}{8}) \\ = \frac{1}{3} - \frac{7}{24} \\ = \frac{1}{24} \\ A's wages:B's wages:C's wages \\ = \frac{1}{6} : \frac{1}{8} : \frac{1}{24} \\ = 4 : 3 : 1 \\ ∴ C's share (for 3 days) \\ = R s . (3 \times \frac{1}{24} \times 3200) \\ = R s . 400 \end{aligned}$

200.

A can build a wall in the same time in which B and C together can do it. If A and B together can do it. If A and B together could do it in 25 days and C alone in 35 days, in what time could B alone do it ?

(A) 91 days
(B) 100 days
(C) 175 days
(D) None of these

Solution: $\begin{aligned} (A + B)'s 1 day's work = \frac{1}{25} \\ C's 1 day's work = \frac{1}{35} \\ (A + B + C)'s 1 day's work \\ = (\frac{1}{25} + \frac{1}{35}) \\ = \frac{12}{175} . . . . . (i) \end{aligned}$ Also, A's 1 day's work = (B + C)'s 1 day's work.....(ii) $\begin{aligned} From (i) and (ii), we get : \\ \Rightarrow 2 \times (A's 1 day's work) = \frac{12}{175} \\ \Rightarrow A's 1 day's work = \frac{6}{175} \\ ∴ B's 1 day's work \\ = (\frac{1}{25} - \frac{6}{175}) \\ = \frac{1}{175} \end{aligned}$

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Practice MCQ Questions and Answer on Time and Work

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