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12251.

________ people came than I expected. A) Other B) Fewer C) Another D) Few

Answer»

Correct option is B) Fewer

12252.

When Peter told ___ about ___ I didn’t believe ___ . A) her/her/her B) they/me/them C) him/it/her D) me/it/him E) us/you/her

Answer»

Correct option is D) me/it/him

12253.

If you’ve read my book, please ________ to me. A) give it again B) give again it C) give it back D) give back it

Answer»

Correct option is C) give it back

12254.

Let ___ take ___ book, please. A) his/her B) him/his C) him/your D) me/him E) I/my

Answer»

Correct option is C) him/your

12255.

Could you give ___ book to ___ please. She has forgotten to take ___ . A) her/your/hers B) your/her/hers C) my/my/mine D) him/his/theirs E) it/him/its

Answer»

Correct option is B) your/her/hers

the correct option is -your/her/hers

12256.

Oxygen atom in ether isA. very activeB. replaceableC. activeD. comparatively inert

Answer» Correct Answer - D
The divalent oxygen is linked strongly to C- atoms on both sides and there are no active sites like `OH. CO=O`etc.in it.
12257.

Write the Duties and responsibilities of inventory Control Supervisor.

Answer»

Duties: 

1. Coordinates staff, processes and procedure to support the DC in maintaining and exceeding inventory accuracy goals. 

2. Analyze data and publish reports. 

3. Maintain system data integrity. 

4. Track performance by area, determine problems and root causes. 

5. Implement and administer all approved changes to current inventory program

Responsibilities:

1. Coordinate and perform physical inventories of daily/weekly cycle accounts and adjusts inventory records if necessary. 

2. Investigate inventory variances. 

3. Perform other related duties as assigned by management. 

4. Review and monitor the timely confirmation and accuracy of inbound inventory and outbound shipments.

12258.

Calculate the number of coulombs required to deposit `2.7 xx 10^(-2) kg` of aluminium when the electrode reaction is `A1^(3+ ) + 3e^(-) "to" A1` (Given : Atomic weight of A1= 27 g `"mol"^(-1)`

Answer» Quantity of electricity = Q= 289500 C`
12259.

Hybrid state of central oxygen atom in ether isA. `sp^(2)`B. `sp^(3)`C. `sp`D. `sp^(3)d`

Answer» Correct Answer - B
See comprehensive Review.
12260.

Grignard reagents are prepared inA. BenzeneB. ChloroformC. AlcoholsD. Ethers

Answer» Correct Answer - D
Ether stabilise R-MgX by forming coordinate bonds with Mg atom.
12261.

आईपीएल में किस टीम ने सर्वाधिक जीत हासिल की है?a.   राजस्थानb.   मुंबई इंडियंसc.   दिल्ली कैपिटल्सd.   हैदराबाद

Answer»

सही विकल्प है b. मुंबई इंडियंस

12262.

आईपीएल के इतिहास में सबसे ज्यादा शतक जड़ने का रिकॉर्ड किसके नाम दर्ज है?a.   विराट कोहलीb.   के एल राहुलc.   क्रिस गेलd.   शिखर धवन

Answer»

सही विकल्प है c. क्रिस गेल

12263.

आईपीएल 2020 का आयोजन किस देश में किया गया?a.   भारतb.   यूएसएc.   यूएईd.   ऑस्ट्रेलिया

Answer»

सही विकल्प है c. यूएई

12264.

IPL 2020 में ऑरेंज कैप किस खिलाड़ी को मिली है?a.   ईशान किशनb.   के एल राहुलc.   डेविड वार्नर  d.   शिखर धवन

Answer»

सही विकल्प है   b. के एल राहुल
 670 रन बनाये।

 

12265.

IPL 2020 में पर्पल कैप विजेता कौन सा खिलाड़ी है?a.   कागिसों रबादाb.   जसप्रीत बूमराहc.   ट्रेंट बोल्टd.   यजुवेन्द्र चहल

Answer»

सही विकल्प है a. कागिसों रबादा

12266.

IPL में लगातार दो शतक लगाने वाला प्लेयर कौन है?a.   विराट कोहलीb.   के एल राहुलc.   शिखर धवनd.   मयंक अग्रवाल 

Answer»

सही विकल्प है c. शिखर धवन

12267.

Solve the followingdifferential equation :`(dy)/(dx)+2y=6e^x`

Answer» `dy/dx=P(x)=Q(x)`
`IF=e^(intP(x)dx`
`IF=e^(2dx)=e^(2x)`
`y*(IF)=int(Q(x)IFdx``yxe^(2x)=int(6e^x)*e^(2x)dx`
`y*e^(2x)=6inte^(3x)dx`
`y*e^(2x)=6*e^(3x)/3+c`
`y=2e^(x)+e^(-2x)C`.
12268.

IPL 2020 में गेम चेंजर ऑफ द सीजन खिताब किसने जीता है?a.   कागिसों रबादाb.   जोफ्रा आर्चरc.   ईशान किशनd.   के एल राहुल

Answer»

सही विकल्प है d. के एल राहुल

12269.

IPL 2020 में सबसे ज्यादा छक्के किस खिलाड़ी ने लगाये हैं?a.   शिखर धवनb.   ईशान किशनc.   के एल राहुलd.   संजू सेमसन

Answer»

सही विकल्प है b. ईशान किशन

12270.

IPL 2020 में इमर्जिग प्लेयर ऑफ सीजन कौन बना है?a.   के एल राहुलb.   शिखर धवनc.   देवदत्त पल्तीकलd.   यजुवेन्द्र चहल

Answer»

सही विकल्प है c. देवदत्त पल्तीकल

12271.

IPL 2020 में सबसे पहला शतक किस खिलाड़ी ने लगाया?a.   के एल राहुलb.   शिखर धवनc.   विराट कोहलीd.   मयंक अग्रवाल  

Answer»

सही विकल्प है  a.  के एल राहुल

12272.

How are integrated steel plants different from mini steel plants?

Answer»

Following are the points of distinction:

(a) An integrated steel plant is larger than mini steel plant.

(b) Mini steel plant uses steel scrap and sponge iron while integrated steel plant use basic raw materials, i.e. iron ore for making steel.

(c) Mini steel plant produces mild and alloy steel while integrated steel plant produces only steel

12273.

What are the expected 4 gross motor skills and 4 fine motor skills of 3-6 year old children?

Answer»

Gross Motor skills 

  • Becoming more skilled at running, jumping, early throwing, and kicking 
  • Catching a bounced ball 
  • Pedaling a tricycle (at 3 years); becoming able to steer well at around age 4 
  • Hopping on one foot (at around 4 years), and later balancing on one foot for up to 5 seconds 

Fine Motor Skills 

  • Drawing a circle 
  • Drawing a person with 3 parts 
  • Beginning to use children's blunt-tip scissors 
  • Self-dressing (with supervision)
12274.

Write a brief note on sports injuries and it's causes

Answer»

Types of sports injuries include:

  • Sprains. Overstretching or tearing the ligaments results in a sprain.
  • Strains. Overstretching or tearing muscles or tendons results in a sprain.
  • Knee injuries.
  • Swollen muscles.
  • Achilles tendon rupture.
  • Fractures.
  • Dislocations.
  • Rotator cuff injury.
12275.

Which test is used to measure the fitness level?

Answer»
  • Chair Stand Test - testing lower body strength
  • Arm Curl Test - testing upper body strength
  • Chair sit and Reach Test - lower body flexibility test
  • Back Scratch Test - upper body flexibility test
  • 8 Foot Up and Go Test - agility test
  • Walk Test (6 min) - used to assess aerobic endurance
12276.

Write a brief note on sports injuries and enlist it's causes

Answer»

Types of sports injuries include:

  • Sprains. Overstretching or tearing the ligaments results in a sprain.
  • Strains. Overstretching or tearing muscles or tendons results in a sprain.
  • Knee injuries.
  • Swollen muscles.
  • Achilles tendon rupture.
  • Fractures.
  • Dislocations.
  • Rotator cuff injury.
12277.

Find the word which is out of the logic list:A) face B) crouch C) come across D) encounter

Answer»

Correct option is B) crouch

12278.

दो संख्याए `3:5` के अनुपात में है। और प्रत्येक संख्या में 10 जोड़ा जाता है तो अनुपात `5:7` हो जाता है। तो छोटी संख्या ज्ञात करो।A. 9B. 12C. 15D. 25

Answer» Correct Answer - C
`{:(,A,:, B),(,3,:, 5),("Let", 3x,:, 5x):}`
(प्रत्येक संख्या में 10 जोड़ने पर)
` implies (A)/(B)=(3x+10)/(5x+10)=(5)/(7)`
21x+70=25x+50
4x=20
x=5
` therefore A=3xx5=15`
`implies B=5xx5=25`
Smaller number=15
12279.

दो संख्याए `3:5` के अनुपात में है। यदि उन दोनों में 6 जोड़ दिया जाए, तो अनुपात `2:3` हो जाता है। वे संख्याएँ क्या है?A. 21 and 35B. 30 and 50C. 25 and 40D. 18 and 30

Answer» Correct Answer - D
Let no. are =3x and 5x
`therefore` According to question
`(3x+6)/(5x+6)=(2)/(3)`
9x+18=10x+12
x=6
So numbers are
`3x=3xx6=18`
`5x=5xx6=30`
12280.

Tangents, parallel to angle bisector of lines `lx+my+n=0` and `ax +by +c=0` are drawn to ellipse `(x^(2))/(36)+(y^(2))/(64)=1`, so as to generate a quadrilateral with vertices as points of intersection of these tangents and inscribing the ellipse. Then the maximum area of the quadrilateral is-A. `100`B. `200`C. `300`D. `400`

Answer» Correct Answer - B
Any pair of angle bisectors of real and intersecting lines are perpendicular to each other.
Hence the tangents which are obtained will be opposite pair wise parallel and adjacent pair wise perpendicular.
Hence the quadrilaternal will be a rectangle.
Also vertices of this rectangle will lie on the director circle of the ellipse, Which is
Of all the rectangle that can be inscribed in this circle the maximum area is of the one which is a square having area 200.
This square is easily observed when vertices lie on the co-ordinate axes.
Ans.200`
12281.

Consider the parabola `y^(2)=8x,` if the normal at a point P on the parabola meets it again at a point Q, then the least distance of Q from the tangent at the vertex of the parabola isA. `16`B. `8`C. `0`D. None of these

Answer» Correct Answer - A
`P-=(at_(1)^(2),2at_(1)),Q-=(at_(2)^(2),2at_(2))`, then
`t_(2)=-t_(1)-(2)/(t_(1))`
Here `4a =8" " therefore a=2`
Required distance,
`z=at_(2)^(2)=2(t_(1)^(2)+(4)/(t_(1)^(2))+4)=2[(t_(1)-(2)/(t_(1)))^(2)+8...(i)`
`implies zge2(8)]...(i)`
`therefore "least value of" z=16 ["from" (i)]`
12282.

A factory outlet has decided to dispose of its old stock by selling each set of cups for ₹ 287 and recovering only the variable cost. If the fixed cost is 18% of the total cost, what was the cost price of each set of cups?1. ₹ 3202. ₹ 3503. ₹ 3254. ₹ 340

Answer» Correct Answer - Option 2 : ₹ 350

Given:

SP of each set = Rs. 287

Fixed cost = 18% of total cost

Explanation:

There is a loss of 18 %

∴ SP is 82% of CP

82% of CP = Rs. 287

CP = Rs. (287/82) × 100

⇒ Rs. 350

∴ The cost price of each set of cup is Rs. 350

12283.

1 cup costs Rs. 80 but a box containing 6 cups costs Rs. 400. What is the effective discount (in %) on the box?1. 10%2. 15%3. 16.67%4. 20%

Answer» Correct Answer - Option 3 : 16.67%

GIVEN:

1 cup costs Rs. 80 but a box containing 6 cups costs Rs. 400.

CONCEPT:
Basic concept of discount.

FORMULA USED:

Discount = [(MP – SP)/MP] × 100

CALCULATION:

Original cost of 6 bars of chocolates = 6 × 80 = Rs. 480

∴ Effective discount on the box = [(480 – 400)/480] × 100

= 16.67%

12284.

Akash had two cups which he purchased for Rs 390 and 460 respectively. Upon selling the second cup at Rs. 575, he made a total profit of 245 on both the cups. If the profit percentage for the two cups is interchanged, find his total profit (in Rs.).1. 204.832. 224.833. 264.834. 250.83

Answer» Correct Answer - Option 4 : 250.83

Given:

Akash purchased two cups for Rs 390 and 460 respectively.

Upon selling the second cup at Rs. 575, he made a total profit of 245 on both the cups. 

The profit percentage for the two cups is interchanged.

Formula Used:

Profit or Gain = Selling price – Cost Price

Loss = Cost Price – Selling Price

Profit percentage = (Profit /Cost Price) x 100

Loss percentage = (Loss/Cost price) x 100

Calculation:  

1st 2nd
390  460 (Cost Price)
520  575 (Selling price)
130  115 (profit)
33.33 25 (p%)
25  33.33 (new p%)

                  

1st profit = Rs. (390 × 1/4) = Rs. 97.5

2nd profit = Rs. (460 × 1/3) = Rs. 153.33

Total profit = Rs. 250.83

∴ His total profit is Rs. 250.83

12285.

If an amount of Rs.1,72,850 is equally distributed amongst 25 people, how much amount would each person get ?(a) Rs.8912.50      (b) Rs.8642.50(c) Rs.7130           (d) Rs.6914(e) None of these

Answer»

(d) Amount received by each person
172850/25
= Rs.6914

12286.

Find the ratio between √ 432 : √ 6751. 4 : 52. 5 : 73. 3 : 44. 2 : 5

Answer» Correct Answer - Option 1 : 4 : 5

√ 432 = 12√ 3 and √ 675 = 15√ 3

Now, √ 432 : √ 675

= 12√ 3 : 15√ 3

= 12 : 15

= 4 : 5

12287.

The sum of four consecutive even numbers. A, B, C, and D is 180. What is the sum of the set of next four consecutive even numbers ?(a) 214      (b) 212(c) 196      (d) 204(e) None of these

Answer» (b) A + A + 2 + A + 4 + A + 6 = 180
4A + 12 = 180
A = 42.
Next four consecutive even numbers are
50 + 52 + 54 + 56 = 212
12288.

The sum of a set of five consecutive even numbers is 140. What is the sum of the next set of five consecutive even numbers?(a) 190 (b) 180(c) 200 (d) 160(e) None of these

Answer»

 (a) According to the question, 

x + x + 2 + x + 4 + x + 6 + x + 8 = 140 

or, 5x + 20 = 140 

or, 5x = 120 

x = 120/5 = 24 

x + 8 = 24 + 8 = 32 

The next set of five consecutive even number will start with = 34 

Required sum = 34 + 36 + 38 + 40 + 42 = 190

12289.

A tap can fill up a tank of 1250 litres in 4 hours, whereas another tap can fill the same tank in 8 hours. An outlet tap can empty that tank in 6 hours. If all the three taps are opened simultaneously, then how much time will it take to fill the tank completely?1. 4.2 hours2. 4.5 hours3. 5 hours4. 4.8 hours

Answer» Correct Answer - Option 4 : 4.8 hours

Given:

Tap A can fill a tank in 4 hours

Tap B can fill the same tank in 8 hours

Tap C can empty the same tank in 6 hours

Concept Used: 

If a tap can fill a tank in n hours then part of the tank filled in 1 hour is 1/n

Calculation:

Time is taken by tap A to fill the tank = 4 hours

Tank filled by tap 1 in one hour = 1/4 part of the tank 

Time is taken by tap B to fill the tank = 8 hours

Tank filled by tap 2 in one hour = 1/8 part of the tank 

Time is taken by tap C to empty the tank = 6 hours

Tank emptied by tap 3 in one hour = 1/6 part of the tank 

So, the part of the tank filled in one hour when all three taps are opened simultaneously 

\(\frac{1}{4} + \frac{1}{8} - \frac{1}{6}\;part\)

\( ⇒ \;\frac{{6 + 3 - 4}}{{24}}\;part\)

\(⇒ \;\frac{5}{{24}}\;part\)

⇒ Time taken by 3 taps to fill the tank = 24/5 = 4.8 hours.

∴ time taken by three taps to fill the tank is 4.8 hours.

12290.

In the following number series, a wrong number is given. Find out the wrong number.16, 26, 39, 52, 681. 162. 263. 394. 525. 68

Answer» Correct Answer - Option 3 : 39

Given:

The number series:

16, 26, 39, 52, 68

Concept Used:

Number series following a fixed pattern.

Calculation:

The given number series follows the pattern:

4+ 0 = 16 

52 + 1  = 26

62 + 2 = 36 + 2 = 38

72 + 3 = 49 + 3 = 52

82 + 4 = 64 + 4 = 68

The wrong number in the given number series is 39.

12291.

Find the wrong term in the given series.5, 10, 26, 50, 120, 1701. 1202. 1703. 264. 505. 10

Answer» Correct Answer - Option 1 : 120

22 + 1 = 4 + 1 ⇒  5

32 + 1 = 9 + 1 ⇒  10

52 + 1 = 25 + 1 ⇒ 26

72 + 1 =  49 + 1 ⇒ 50

112 + 1 = 121 + 1 = 122

132 + 1 = 169 + 1 = 170

∴ In the given pattern 120 is the wrong number

12292.

Two friends X and Y started typing work and were hopeful to complete the work in 10 days and 15 days respectively. They started the work together, but due to an emergency, X left after just 5 days and asked his friend Z to join at his place, who could alone complete this work in 60 days. In how many days did the work get completed?1. 142. 63. 74. 5

Answer» Correct Answer - Option 3 : 7

Given:

Time taken by X to complete the work alone = 10 days

Time taken by Y to complete the work alone = 15 days

Time taken by Z to complete the work alone = 60 days

Formula Used:

Efficiency = Total work/Time taken

Calculation:

Let the total work be 60x units (LCM of 10,15, 60)

Efficiency of X = 6x units/day

Efficiency of Y = 4x units/day

Efficiency of Z = x units/day

Work done in 5 days by X and Y = (6x + 4x) × 5

= 50x units

⇒ Remaining work = 60x – 50x = 10x units

This work is completed by Y and Z

Time taken to complete the remaining work = 10x/[(4x + x)]

= 10x/5x = 2 days

Total time taken to complete the whole work = 5 + 2 = 7 days

∴ The total time taken to complete the whole work is 7 days

12293.

A man goes uphill at an average speed of 24 kmph. and comes down at an average speed of 30 kmph., the distance travelled in both the cases being the same. The average speed of the entire journey is1.  30 kmph.2. 30.8 kmph3. 26.6 kmph4. 32.6 kmph

Answer» Correct Answer - Option 3 : 26.6 kmph

Given:

Average of speed during uphill (S1) = 24 kmph

Average of speed during down (S2) = 30 kmph

Formula used:

Average speed = (2 × S1 × S2)/(S1 + S2)

Calculation:

Average speed = (2 × 24 × 30)/(24 + 30)

⇒ 1440/54

⇒ 26.66 kmph

Hence, The average speed of the entire journey is 26.66 kmph.

12294.

P and Q into a partnership for a year. Initial investment of P is Rs. 500 and initial investment of Q is 40% of initial investment of P. After 5 months, P adds half of the initial investment of P and after 4 months, Q adds again Rs. 200. Total profit they had is Rs.2350. Find the difference between their profit shares.1. Rs. 7502. Rs. 6003. Rs. 9004. Rs. 8005. Rs. 500

Answer» Correct Answer - Option 1 : Rs. 750

Given:

⇒ Total investment of P = 500 × 5 + 750 × 7 = Rs.7750

⇒ Initial investment of Q = 500 × 40/100 = Rs.200

⇒ Total investment of Q = 200 × 4 + 400 × 8 = Rs.4000

Ratio oft their profit shares = 7750 : 4000 = 31 : 16

∴ Required difference = 2350 × (31 - 16) /(31 + 16) = Rs.750

12295.

A takes 5 hours to travel 320 km while B takes 7 hours to travel 301 km. Find the time A will take to cover a distance that B covers in 19 hours after reducing his speed by 13 km/hr.1. 8.9 hr2. 9.8 hr3. 7.8 hr4. 8.7 hr

Answer» Correct Answer - Option 1 : 8.9 hr

Given:

A takes 5 hours to travel 320 km while B takes 7 hours to travel 301 km.

Formula Used:

Distance = time x speed

Calculation:

Speed A = (320/5) km/hr = 64 km/hr

Speed of B = (301/7) km/hr = 43 km/hr

Now, distance covered by B in 19 hours after reducing his speed by 13 km/hr = (30 × 19) km = 570 km.

Time required = (570/64) hours = 8.9 hours

∴ A will take 8.9 hours.

12296.

Q and R went into a partnership for a year. The ratio between the initial investment of Q and R is 1 : 4. After 6 months, Q adds Rs.400 to his investment and after 5 months, R removes Rs.200 from his investment. The profit share of Q is Rs.1080. Total profit they had is Rs.2100. Find the initial investment of Q.1. Rs.1002. Rs.4303. Rs.2004. Rs.3005. Rs.150

Answer» Correct Answer - Option 1 : Rs.100

Given:

Let the initial investment of Q and R be Rs.a and Rs.4a respectively.

⇒ Total investment of Q = a × 6 + (a + 400) × 6 = Rs.(12a + 2400)

⇒ Total investment of R = 4a × 5 + (4a - 200) × 7 = Rs.(48a - 1400)

⇒ Profit share of R = 2100 - 1080 = Rs.1020

Then,

⇒ (12a + 2400)/(48a - 1400) = 1080/1020

⇒ (12a + 2400)/(48a - 1400) = 36/34

⇒ (12a + 2400)/(48a - 1400) = 18/17

⇒ a = 100

∴ Initial investment of Q = Rs.100.

 

12297.

Radha and Sham went into a partnership for a year. Radha invests Rs.200 and Sham invests Rs.100. After 4 months, Radha adds Rs.50 to his investment. After 5 months, Sham adds Rs.300 to his investment. Profit they had in a year is Rs.915. Find the profit share of Sham.1. Rs.6802. Rs.5803. Rs.3804. Rs.4105. Rs.495

Answer» Correct Answer - Option 5 : Rs.495

Given:

⇒ Total investment of Radha = 200 × 4 + 250 × 8 = Rs.2800

⇒ Total investment of Sham = 100 × 5 + 400 × 7 = Rs.3300

Ratio of their profit shares = 2800 : 3300 = 28 : 33

∴ Profit share of Sham = 915 × 33/(28 + 33) = Rs.495

12298.

Raju and Ramu went into a partnership for a year. Raju invests Rs.250 and Ramu invests some amount. After 7 months, Raju adds Rs.150 and Ramu removes Rs.150 to their respective investment. Total profit they had is RS.2800. The difference between their profit shares is Rs.300. Find the initial investment of Ramu. (Ramu share is 300 more than Raju)1. Rs.6002. Rs.4503. Rs.3004. Rs.5005. Rs.560

Answer» Correct Answer - Option 2 : Rs.450

Given:

Let initial investment of Ramu be Rs.a.

⇒ Total investment of Raju = 250 × 7 + 400 × 5 = Rs.3750

⇒ Total investment pf Ramu = a × 7 + (a - 150) × 5 = Rs.(12a - 750)

Total profit shares of Raju and Ramu = Rs.2800

The difference between the profit shares = 300

Solving,

⇒ The profit share of Raju = Rs.1250

⇒ The profit share of Ramu = Rs.1550

Then,

⇒ 3750 : (12a - 750) = 1250 : 1550

⇒ a = 450

∴ Initial investment of Ramu is Rs.450.

12299.

Shubham travels some distance. He travels (1/3)rd of the total distance with a speed of 25 km/h in 2 hours. Find the total distance travel by Shubham.1. 140 km2. 120 km3. 180 km4. 150 km

Answer» Correct Answer - Option 4 : 150 km

Given:

(1/3)rd of distance travel with speed 25 km/h.

Formula used:

Speed = Distance/Time

Calculation:

Let the total distance is x km

25 = [(x/3)/(2)]

⇒ 25 = (x/6)

⇒ x = 150 km 

12300.

Raj and Ram went into a partnership for a year. Raj invests Rs.500 and Ram invests Rs.100 more than Raj. After 8 months, Raj removes some amount and Ram adds same amount to his investment. The profit share of Raj is Rs.1040. The average profit share of Raj and Ram is Rs.1320. Find the amount removed and added by Raj and Ram after 8 months.1. Rs.2802. Rs.2003. Rs.1504. Rs.1005. Rs.220

Answer» Correct Answer - Option 2 : Rs.200

Given:

Let amount removed and added by Raj and Ram after 8 months be Rs.a.

⇒ Total investment of Raj = 500 × 8 + (500 - a) × 4 = Rs.(6000 - 4a)

⇒ Total investment of Ram = 600 × 8 + (600 + a) × 4 = Rs.(7200 + 4a)

Total profit shares of Raj and Ram = Rs.2640

⇒ The profit share of Ram = 2640 - 1040 = Rs.1600

Then,

⇒ (6000 - 4a) : (7200 + 4a) = 1040 : 1600

Solving,

⇒ a = 200

∴ After 8 months, Raj and Ram removed and added Rs.200.