Answer: Option D
Explanation: A and B together finish a piece of work = x = 4 days
A alone finish a piece of work = y = 12 days.
By the short trick approach:
B alone can do the whole work in \(\frac{4 × 12}{12 – 4}\)
= \(\frac{40}{4}\) = 6 days
2. 6 women can complete a piece of work in 10 days, whereas 10 children alone take 15 days to complete the same piece of work. How many days will 6 women and 10 children together take to complete the piece of work?
Answer: Option C
Explanation:
6 Women’s 1 day’s work = \(\frac{1}{10}\);
10 Children’s 1 day’s work = \(\frac{1}{15}\);
(6 women + 10 children)’s 1 day’s work = \(\frac{1}{10}\) + \(\frac{1}{15}\)
= \(\frac{5}{30}\)
= \(\frac{1}{6}\)
So, total time taken to complete work = 16 + 6= 22 hrs.
3. Salim taken 8 days to finish a piece of work. Manoj takes 12 days to finish the same piece of work. Raj works twice as fast as Salim. How many days will all three of them together take to finish the same piece of work?
Answer: Option D
Explanation: Time taken by Salim = x = 8 days
Time taken by Manoj = y = 12 days
Time taken by Raj (Twice as fast as Salim) = z = 8/2 = 4 days
By the short trick approach:
A, B and C can do the work in \(\frac{8 × 12 × 4}{8 × 12 + 12 × 4 + 4 × 8}\) \(\frac{×yz}{xy+yz+ zx }\)
After taking 8 as a common term we get,
\(\frac{48}{12 + 6 + 4}\)
= \(\frac{48}{22}\)
= \(\frac{24}{11}\)
= 2\(\frac{2}{11}\)days
4. A and B together can finish a work in 9 days. A alone can finish the work in 12 days. In how many days will B alone finish the work?
Answer: Option D
Explanation: Time taken by A and B together to finish a piece of work = x = 9 days
Time taken by A alone to finish the same piece of work = y = 12 days.
By the short trick approach:(\(\frac{xy}{x – y}\))
B alone can do the whole work in \(\frac{12 × 9}{12 – 9}\) = \(\frac{108}{3}\) = 36 days
5. P can finish a work in 25 days and Q can do the same work in 20 days. Q worked for 8 days and left the job. In how many days, P alone can finish the remaining work?
Answer: Option C
Explanation: Q’s 8 days work =[ \(\frac{1}{20}\) x 8] work ⇒ \(\frac{2}{5}\)
Remaining work = [1 –\(\frac{2}{5}\)]
Now, \(\frac{1}{25}\) work is done by P in 1 day
∴ \(\frac{3}{5}\) work is done by P in [25 x \(\frac{3}{5}\)]
Answer: Option A
Explanation:
(Nitin + Nirdosh)’s 1 day’s work = \(\frac{1}{6}\)
Nitin’s 1 day’s work = \(\frac{1}{24}\)
∴ Nirdosh’s 1 day’s work \(\frac{1}{6}\) – \(\frac{1}{24}\)⇒ \(\frac{3}{24}\)
⇒ \(\frac{1}{8}\)
2. A, B and C together earn Rs. 300 per day, while A and C together earn Rs. 188 and B and C together earn Rs. 152. The daily earning of C is:
Answer: Option A
Explanation: B’s daily earning = Rs. (300 – 188) = Rs. 112.
A’s daily earning = Rs. (300 – 152) = Rs. 148.
C’s daily earning = Rs. [300 – (112 + 148)] = Rs. 40
3. 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
Answer: Option D
Explanation: 1 man’s 1 day’s work
\(\frac{1}{100}\) , (10 men + 15 women)’s 1 day’s work = \(\frac{1}{6}\)
15 women’s 1 day’s work [\(\frac{1}{6}\) – \(\frac{10}{100}\)] = [\(\frac{1}{6}\) – \(\frac{1}{10}\)] = \(\frac{1}{15}\)
∴ 1 woman’s 1 day’s work = \(\frac{1}{125}\)
Then, 1 woman alone can complete the work in 225 days.
4. A girl can do a job in 10 days, Her mother takes 25 days and her sister finishes it in 20 days. How long will they take to complete the job if they all together?
Answer: Option C
Explanation: 1 day’s work of the three persons
= [\(\frac{1}{10}\) +\(\frac{1}{25}\)+\(\frac{1}{20}\) ] ⇒
(\(\frac{10 + 4 + 5 }{100}\))= \(\frac{19}{100}\)
Hence, the printing of books will be completed at 5(\(\frac{1}{11}\))hours
So all the three together will complete the work in \(\frac{100}{19}\) = 5.3 days
5. A and B together can complete a piece of work in 12 days, B and C can do it in 20 days and C and A can do it in 15 days. A, B and C together can complete it in
Answer: Option D
Explanation: If A and B can do a piece of work in x days, B and C in y days, C and A in z days, then (A + B + C) working together will do the same work in
\(\frac{2xyz}{xy + yz + zx}\)
A and B together finish a piece work = x = 12 days
B and C together finish a piece work = y = 20 days
C and A together finish a piece work = z = 15 days
By the short trick approach:
A, B and C can do the work in \(\frac{2 × 12 × 20 × 15}{12 × 20 + 20 × 15 + 15 × 12}\) days
After taking 20 as a common term we get, = \(\frac{2 × 12 × 15}{12 + 15 + 9}\) days
After taking 3 as a common term we get, \(\frac{2 × 14 × 15}{4 + 5 + 3}\) days = \(\frac{120}{ 12}\) = 10 days
Answer: Option D
Explanation:
To solve this question, we can apply a short trick approach;
If A working alone takes ‘x’ days more than A and B, and B working alone takes ‘y’ days more than
A & B together then the number of days taken by A & B working together is given by \(\sqrt{xy}\) days.
A’s time = x = 4 days
B’s time = y = 16 days
By the short trick approach:\(\sqrt{4 × 16}\) = \(\sqrt{64}\) = 8 days
2. ‘A’ can do a piece of work in 20 days and ‘B’ can do the same work in 15 days. How long will they take to finish the work, if both work together?
C. 8 × \(\frac{4}{7}\) days
D. 20 days
Answer: Option C
Explanation: A’s time = x = 20 days
B’s time = y = 15 days
By the short trick approach:
A + B can do the work in
8 × \(\frac{20 × 15}{20 + 15}\) days = \(\frac{300}{35}\) = \(\frac{60}{7}\) = 8 × \(\frac{4}{7}\) days
3. Ashokan is thrice as good a workman as Nitin and is therefore able to finish a piece of work in 40 days less than Nitin. Find the time in which they can do it working together.
Answer: Option A
Explanation:If A is ‘n’ times as fast (or slow) as B, and is therefore able to finish a work in ‘D’ days less (or more) than B, then the time in which they can do it working together is given by
Therefore, x = (\(\frac{Dn}{{n}^{2} – 1}\))
Ashokan’s days less then Nitin = D = 40 days
Ashokan is 3 times as fast as Nitin = n = 3.
By the short trick approach:
we have the Required answer \(\frac{40 × 3}{{3}^{2} – 1}\)
= \(\frac{40 × 3}{8} \) = 15 days
4. A completes a piece of work in 4 days and B completes it in 6 days. If they both work on it together, then the number of days required to complete the same work is
Answer: Option C
Explanation:A’s time = x = 4 days
B’s time = y = 6 days
By short trick approach:
A + B can do the work in = \(\frac{4 × 6}{4 + 6}\)days
\(\frac{24}{10}\) = 2\(\frac{2}{5}\) days
5. A is twice as good a workman as B and together they finish a piece of work in 14 days. The number of days taken by A alone to finish the work is
Answer: Option B
Explanation: By the short trick approach:
A finish the work in \(\frac{2 + 1}{2}\)× 14 = 21 days [\(\frac{n + 1}{2}\) x (n + 1)x ]
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