3 workers Peroola, Rahul and Prashant can complete a piece of work in 6 days. Peroola takes 15 days less than Rahul to complete the same work. Find in how many days will Prashant complete the whole work alone with 75% of his original efficiency, if Rahul can complete the work alone in 35 days?
(Peroola + Rahul + Prashant)’s one day work = 70 units
Peroola’s one day work = 21 units
⇒ Rahul = 12 units
Prashant’s one day work = 70 – 33 = 37 units
Prashant’s efficiency to do the work alone
=
75
× 37
100
Time required to complete the work
=
420 × 4
=
560
days
37 × 3
37
Hence, option A is correct.
1
3 कार्यकर्ता पेरुला, राहुल और प्रशांत 6 दिनों में काम पूरा कर सकते हैं। उसी काम को पूरा करने में पेरुला को राहुल से 15 दिन कम समय लगता है। ज्ञात करें कि कितने दिनों में प्रशांत अपनी मूल दक्षता के 75% के साथ पूरे काम को पूरा करेगा, अगर राहुल अकेले 35 दिनों में काम पूरा कर सकता है?
(Peroola + Rahul + Prashant)’s one day work = 70 units
Peroola’s one day work = 21 units
⇒ Rahul = 12 units
Prashant’s one day work = 70 – 33 = 37 units
Prashant’s efficiency to do the work alone
=
75
× 37
100
Time required to complete the work
=
420 × 4
=
560
days
37 × 3
37
Hence, option A is correct.
A
2
Three persons A , B, and C complete a piece of work in 6 days for which they are paid a sum of Rs. 480.If the efficiency of A, B and C are in ratio 4 : 5 :7, then find the daily income of B?
Total amount earned by A ,B, and C in 6 days =Rs 480
The amount earned by them in 1 day =
480
= Rs 80
6
Amount of money earned is proportional to the amount of work done
Let work done by A ,B and C be 4x, 5x and 7x.
∴ Total work done by A,B and C together= 16x
Work done by B = 5x
Daily income of B =
5x
× 80 = Rs. 25
16x
Hence, option A is correct.
2
तीन व्यक्ति A, B और C 6 दिनों में एक काम पूरा करते हैं, जिसके लिए उन्हें 480 रुपये का भुगतान किया जाता है। यदि A, B और C की दक्षता 4: 5: 7 के अनुपात में है, तो B की दैनिक आय का पता लगाएं?
Total amount earned by A ,B, and C in 6 days =Rs 480
The amount earned by them in 1 day =
480
= Rs 80
6
Amount of money earned is proportional to the amount of work done
Let work done by A ,B and C be 4x, 5x and 7x.
∴ Total work done by A,B and C together= 16x
Work done by B = 5x
Daily income of B =
5x
× 80 = Rs. 25
16x
Hence, option A is correct.
A
3
Rashmi and Pallavi can make a carpet in 3 days and 12 days more than the time taken if both of them worked together. Find the time in which Rashmi can make the carpet alone.
Let the time both of them together will take to make the carpet be x days
Time taken by Rashmi alone = x + 3 days
Time taken by Pallavi alone = x + 12 days
One day work when they both work together = Sum of their individual per day work
1
=
1
+
1
x
x + 12
x + 3
1
=
2x + 15
x
x2 + 15x + 36
x2 + 15x + 36 = 2x2 + 15x
x = 6
Time taken by Rashmi to make carpet alone = 6 + 3 = 9 days
Hence, option A is correct.
3
रश्मि और पल्लवी को जितना समय साथ काम करने में लगता है उससे दोनों को क्रमश: 3 दिन और 12 दिन का अधिक समय एक कालीन बनाने में लगता है। उस समय का पता लगाएं जिसमें रश्मि कालीन को अकेले बना सकती है।
Let the time both of them together will take to make the carpet be x days
Time taken by Rashmi alone = x + 3 days
Time taken by Pallavi alone = x + 12 days
One day work when they both work together = Sum of their individual per day work
1
=
1
+
1
x
x + 12
x + 3
1
=
2x + 15
x
x2 + 15x + 36
x2 + 15x + 36 = 2x2 + 15x
x = 6
Time taken by Rashmi to make carpet alone = 6 + 3 = 9 days
Hence, option A is correct.
A
4
Three workers Trump, Putin and Jinping are appointed to do a job. They together started the job but Jinping left after 3 days when 37% of the job was done. The remaining job was completed by Trump and Putin in 7 days. The ratio of efficiency of Trump and Putin is 4 : 5. Find the number of days required by the slowest worker to complete the entire job alone?
Let x, y and z are the one day’s work of Trump, Putin and Jinping respectively.
According to the question,
⇒ 3 × (x + y + z) = 37% of the work
⇒ 7 × (x + y) = 63%
⇒ x + y = 9%
∵ The ratio of efficiency of Trump and Putin is 4 : 5,
∴ 5x = 4y and x = 4%, y = 5% work per day.
It implies Trump can complete the job and in 25 days and Putin in 20 days.
In 3 days (x + y + z) do 37% of the work
Out of this Trump and Putin would do 27% work = (3 × 9%) of the work.
Remaining work = 37% – 27% = 10% (done by Jinping in 3 days)
∴ The work of z =
10
= 3.33% work per day
3
∴ Jinping is the slowest and he would do the work in 30 days.
Hence, option E is correct.
4
तीन श्रमिकों ट्रम्प, पुतिन और जिनपिंग को नौकरी करने के लिए नियुक्त किया जाता है। उन्होंने एक साथ नौकरी शुरू की लेकिन जिनपिंग ने 3 दिन के बाद नौकरी छोड़ दी जब 37% नौकरी हो चुकी थी। शेष नौकरी को ट्रम्प और पुतिन ने 7 दिनों में पूरा किया। ट्रम्प और पुतिन की क्षमता का अनुपात 4: 5 है। सबसे धीमी गति से काम करने वाले को अकेले पूरे काम को पूरा करने के लिए कितने दिनों की आवश्यकता है?
Let x, y and z are the one day’s work of Trump, Putin and Jinping respectively.
According to the question,
⇒ 3 × (x + y + z) = 37% of the work
⇒ 7 × (x + y) = 63%
⇒ x + y = 9%
∵ The ratio of efficiency of Trump and Putin is 4 : 5,
∴ 5x = 4y and x = 4%, y = 5% work per day.
It implies Trump can complete the job and in 25 days and Putin in 20 days.
In 3 days (x + y + z) do 37% of the work
Out of this Trump and Putin would do 27% work = (3 × 9%) of the work.
Remaining work = 37% – 27% = 10% (done by Jinping in 3 days)
∴ The work of z =
10
= 3.33% work per day
3
∴ Jinping is the slowest and he would do the work in 30 days.
Hence, option E is correct.
E
5
A group of men decided to do a job in 4 days, but 20 men dropped out everyday. Find the number of men who initially decided to do the job, if job was completed in 7 days?
पुरुषों के एक समूह ने 4 दिनों में एक काम करने का फैसला किया, लेकिन 20 पुरुष हर दिन काम को छोड़ कर चले जाते हैं। उन पुरुषों की संख्या ज्ञात करें जिन्होंने शुरू में काम करने का फैसला किया था, अगर काम 7 दिनों में पूरा हो जाता है?
