111.P and Q together can complete a work in 20 days. If P alone can complete the same work in 36 days, then in how many days Q alone can complete the same work?

P और Q एकसाथ एक काम को 20 दिनों में पूरा कर सकते हैं। यदि P अकेले समान काम को 36 दिनों में पूरा करता है, तो Q अकेले समान काम को कितने दिनों में पूरा कर सकता है?


Option”C” is correct

Let work be L.C.M. of 20 and 36 i.e. 180 units

P and Q together work in one day = 180/20 = 9 units

P work in one day = 180/36 = 5 units

→ Q work in one day = (9 – 5) = 4 units

→ So, time taken by Q to complete work = 180/4 = 45 days.

112. A can plough a square field of side 10 m in 10 hours and that can be done by B in 5 hours. In how much time a new field having 50% larger side and square in shape is ploughed if A and B plough together?

A, 10 मीटर के एक वर्गाकार खेत को 10 घंटे में जोत सकता है और यह B द्वारा 5 घंटे में किया जा सकता है। 50% बड़ी भुजा होनेवाला एक नया वर्गाकार खेत A और B कितने समय में एक साथ जोत सकते हैं?


Option”B” is correct

Area of the field to be ploughed = (side)2 = 100 m2

The efficiency of A to plough the field = (Area of field) / (Total Time)

⇒ 100 / 10 = 10 m2 / hour        —(1)

The efficiency of B to plough the field = (Area of field) / (Total Time)

⇒ 100 / 5 = 20 m2 / hour        —(2)

Length of side of new field = 10 + {10 × (50 / 100)}

⇒ 10 + 5 = 15 m

Area of new field = (side)2

⇒ 152 = 225 m2

Colletive efficiency of A and B = (10 + 20) m2 / hour        —(By adding (1) and (2))

⇒ 30 m2 / hour

Total time taken by A and B to plough together = (Area of field) / (Collective efficiency of A and B)

⇒ 225 / 30

⇒ 7.5 hours

∴ A and B will take 7.5 hours to plough the new field.

113. Uma is 45% more efficient than Diksha, and Diksha takes 63 days more than Uma to complete a piece of work. How many days will Uma take to complete the same work?

उमा, दीक्षा से 45% अधिक दक्ष है, और दीक्षा एक कार्य को पूरा करने में उमा की तुलना में 63 दिन अधिक लेती है। उमा को उसी कार्य को पूरा करने में कितने दिन लगेंगे?


Option”C” is correct

The ratio of efficiency of Uma and Diksha = 145 ∶ 100

The ratio of time taken by Uma and Diksha = 100 ∶ 145

Let Uma take 100x days, and Diksha takes 145x days to complete a piece of work.

Days taken by Diksha – Days taken by Uma = 63

⇒ 145x – 100x = 63

⇒ 45x = 63

⇒ x = 63/45

⇒ x = 7/5

Days taken by Uma = 100x

⇒ 100 × 7/5

⇒ 20 × 7

⇒ 140 days

∴ Uma will take 140 days to complete the same work.

114. 3 men and 5 boys can complete a task in 15 days, whereas 6 men and 7 boys can complete the same task in 9 days. Find the relationship between the task done by the boys and the task done by the men.

3 पुरुष और 5 लड़के एक कार्य को 15 दिनों में पूर्ण कर सकते हैं, जबकि 6 पुरुष और 7 लड़के उसी कार्य को 9 दिनों में पूर्ण कर सकते हैं। लड़कों द्वारा किए गए कार्य और पुरुषों द्वारा किए गए कार्य के बीच संबंध ज्ञात कीजिये।


Option”A” is correct

Let efficiency of 1 man and 1 boy be x and y respectively,

According to the question

(3x + 5y) × 15 = (6x + 7y) × 9

⇒ 45x + 75y = 54x + 63y

⇒ 54x – 45x = 75y – 63y

⇒ 9x = 12y

⇒ x : y = 4 : 3      —-(i)

Let’s check the option

Option 1: 3x = 4y

From (i), we get

3 × 4 = 4 × 3

⇒ 12 = 12

∴ Option 1 is correct 

115. A and B can complete a task in 12 days. However, A had to leave a few days before the task was completed and hence it took 16 days in all to complete the task. If A alone could complete the work in 21 days, how many days before the work getting over did A leave?

A और B एक कार्य को 12 दिनों में पूरा कर सकते हैं। हालाँकि, A को कार्य पूरा होने से कुछ दिन पहले छोड़ना पड़ा और इसलिए कार्य को पूरा करने में कुल 16 दिन लगे। यदि A अकेले काम को 21 दिनों में पूरा कर सकता है, तो काम खत्म होने से कितने दिन पहले A ने काम छोड़ दिया?


Option”A” is correct

Given A alone can complete the work in 21 days

A and B together can complete the same work in 12 days

⇒ Total work = L.C.M of (12, 21) = 84

⇒ One day work of A = 4

⇒ One day work of (A + B) = 7

⇒ One day work of B = 3

Let A worked for x days and B worked for 16 days

⇒ 4x + 3 × 16 = 84

⇒ x = 9 days

∴ A left the work before (16 – 9 =) 7 days.

116. If 3 men and 4 boys can do a piece of work in 6 days and 6 men and 3 boys can do it in 4 days. Compare the efficiency of a man to that of a boy

यदि 3 आदमी और 4 लड़के कार्य के एक भाग को 6 दिनों में पूरा कर सकते हैं तथा 6 आदमी और 3 लड़के इसे 4 दिनों में पूरा कर सकते हैं। एक आदमी की कार्यक्षमता की एक लड़के की कार्यक्षमता से तुलना कीजिए।


Option”B” is correct

Suppose the efficiency of a man = x/day

Efficiency of a boy = y/ day

According to problem,

⇒ (3x + 4y) × 6 = (6x + 3y) × 4

⇒ 18x + 24y = 24x + 12y

⇒ 6x = 12y

⇒ x ∶ y = 2 ∶ 1

∴ Ratio of efficiency of a man to that of a boy = 2 ∶ 1

117.A, B and C can complete a work alone in 400, 600 and 900 days respectively. In how many days can the work be completed if it is started by A and he is assisted by B and C on every second and third day respectively?

केवल A, B और C एक काम को क्रमशः 400, 600 और 900 दिनों में पूरा कर सकते हैं। यदि काम A द्वारा प्रारंभ किया गया और उसे क्रमशः प्रत्येक दूसरे और तीसरे दिन B और C द्वारा सहायता प्रदान की गयी, तो काम को कितने दिनों में पूरा किया जा सकता है?


Option”A” is correct

Given that,

A, B and C can complete a work alone in 400, 600 and 900 days respectively,

LCM of 400, 600 and 900 will be 3600.

A’s one day work = 9 units

B’s one day work = 6 units

C’s one day work = 4 units

A : (A + B) : (A + C) = 9 : 9 + 6 : 9 + 4 ⇒ 9 : 15 : 13 = 37 units

3 days = 37 units

The will be completed in 3600/37 × 3 = 291.90 ∼ 292 days

Note: The solution has been modified.

118. A group of 25 women is supposed to do work in 40 days. After 16 days 5 more women are employed and the work is completed in 4 days before the scheduled time. How many days would have been delayed if 5 more women were not employed?

25 महिलाओं के एक समूह को 40 दिनों में एक कार्य करना है। 16 दिनों के बाद 5 और महिलाओं को रोजगार दिया जाता है और यह कार्य निर्धारित समय से 4 दिन पहले पूरा हो जाता है। यदि 5 और महिलाओं को रोजगार नहीं दिया जाता तो कितने दिन की देरी होती?


Option”D” is correct

T is the number of days when 5 more women are not employed

25 × 16 + 30 × 20 = 25 × T

⇒ T = 40, which is equal to previous planned days.

Hence, work is not delayed.

119.In a palace, supplies are available for 35 days for only 75 people. 15 Guests arrive in the place for vacation on day 1 itself. For how many days will these supplies be sufficient for all these people.

किसी स्थान पर, केवल 75 लोगों के लिए 35 दिनों के लिए सामग्री उपलब्ध है। अब उस स्थान पर पहले ही दिन 15 अतिथि छुट्टी मनाने के लिए आते हैं। अब इन सभी के लिए यह सामग्री कितने दिन तक पर्याप्त रह सकेगी।


Option”D” is correct

Let supplies sufficient for x days after coming 15 people.

According to the question

90 × x = 75 × 35

⇒ x = (75 × 35)/90

∴ x = 29.16 days

120. 2 men and 7 women can do a piece of work in 14 days whereas 3 men and 8 women can do it in 11 days. In how many days 5 men and 4 women can do the same work?

2 पुरुष और 7 महिलाएं एक कार्य को 14 दिनों में कर सकते हैं जबकि 3 पुरुष और 8 महिलाएं इसे 11 दिनों में कर सकते हैं। 5 पुरुष और 4 महिलाएं उसी कार्य को कितने दिनों में कर सकते हैं?


Option”A” is correct

⇒ (2m + 7w)14 = (3m + 8w)11

⇒ 28m + 98w = 33m + 88w

⇒ 10w = 5m

⇒ m/w = 2/1

⇒ Total work = (2 × 2 + 7 × 1) × 14

⇒ Total work = 11 × 14

Time taken by 5m and 4 w = (11 × 14)/(5 × 2 + 4 × 1)

⇒ 11 days

∴ Time taken by 5 man and 4 woman is 11 days.

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