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Please help me out in solving this DI caselet.

- 2 Likes
- Let total combined income be I and total combined tax be .... 06 Apr.
- What was the question no 11 ??. 05 Apr.

Let total combined income be I and total combined tax be T. just assume that A will pay 10 % tax and B 20% tax. Note that to calculate the tax of B, 10% will be on 2,00,000 and 20 % on rest income. Just take the ration of taxes of A and B (both in terms of I) and equate it to 1/2 (as evident from the tax pie chart).

Please help me out in solving this DI caselet.

- 7Comments
- 1) 18/26 ?. 05 Apr.
- @clxlfms This is the complete question ji. Is there any w.... 05 Apr.

A K
@clxlfms
477

@airirm let total income be I= Ia+ Ib+ Ic+ Id where ia,b,c,d are incomes of A,BC,D respectively.

Now, TOtal income can also be written as I= 3(Ia+Ib) but I= (100/13.33)*Ia hence => Ia=(2/3)*Ib-----1)

similarly, TOTAL tax=T= 4(Ta+Tb) but T=(100/8.33)*Ta => Tb~ 2 Ta ----------2)

solving them we get Ia post tax/ Ib post tax= 9/13= 18/26

Ps- Some approximations i have taken.

Now, TOtal income can also be written as I= 3(Ia+Ib) but I= (100/13.33)*Ia hence => Ia=(2/3)*Ib-----1)

similarly, TOTAL tax=T= 4(Ta+Tb) but T=(100/8.33)*Ta => Tb~ 2 Ta ----------2)

solving them we get Ia post tax/ Ib post tax= 9/13= 18/26

Ps- Some approximations i have taken.

Please help me out in solving this DI caselet.

- data missign. 07 May.
- @airirm it seems some data is missing... all values are i.... 11 Apr.

Escalators _/\_

(Q1) P and Q walk up a moving up escalator at constant speeds. For every 5 steps that P takes Q takes 3 steps. How many steps would each have to climb when the escalator is switched off, given that P takes 50 and Q takes 40 steps to climb up the moving up escalator respectively?

(1) 80 (2) 90(3) 100 (4) None of these

(Q2) A can take 10 steps per second and B can take 7 steps per second. A mischievously starts climbing down an escalator that is moving upwards and at the same instant B starts climbing up the same escalator. They meet after 5 seconds. If the escalator works at a steady rate of 4 steps per second then how many steps are visible when the escalator is stopped?

(1) 90 (2) 80(3) 85 (4) None of these

(Q3) In the above question, if the escalator was shut off at the instant when A and B meet,both being on different steps with A located above B, then how many steps from the ground is the step on which B stands?

(1) 45 (2) 65(3) 75 (4) 55

- 6Comments
- @garry1337 Ji please share your approach... 26 Feb.
- @airirm Q1) 80 Q2) 85 Q3) 55 Will share the appr.... 26 Feb.

Badri
@garry1337
1.7
k

@airirm For basics refer to this article :

pagalguy.com/news/cat-quant-problems-escalators-time-speed-a-16703950/...

Badri
@garry1337
1.7
k

@airirm

1) Speed of P = 5v Q=3v Escalator =e

Total steps in escalator = Steps covered by P + Steps covered by escalator in that time

50 + e*(50/5v) = 40 + e*(40/3v) ------------------ (1)

e/v = 3

Substitute this back in equation 1

50 + 30 =80 steps

2) A = 10 ; B = 7 ; E = 4

Total steps = 5*(10-4) + 5*(7+4) = 85 steps

3) In 5 sec B would be at 5*(7+4) = 55th step

1) Speed of P = 5v Q=3v Escalator =e

Total steps in escalator = Steps covered by P + Steps covered by escalator in that time

Total steps in escalator = Steps covered by Q + Steps covered by escalator in that time

50 + e*(50/5v) = 40 + e*(40/3v) ------------------ (1)

e/v = 3

Substitute this back in equation 1

50 + 30 =80 steps

2) A = 10 ; B = 7 ; E = 4

Total steps = 5*(10-4) + 5*(7+4) = 85 steps

3) In 5 sec B would be at 5*(7+4) = 55th step

Mr Anderson
@Master-Yoda
626

Q1)

50=5x/(5+v)

40=3x/(3+v)

where x is total step and v is esc speed

Q2) (10-v+7+v)*5

Q3)(7+4)*5=55

50=5x/(5+v)

40=3x/(3+v)

where x is total step and v is esc speed

Q2) (10-v+7+v)*5

Q3)(7+4)*5=55

Escalators _/\_

(Q1) P and Q walk up a moving up escalator at constant speeds. For every 5 steps that P takes Q takes 3 steps. How many steps would each have to climb when the escalator is switched off, given that P takes 50 and Q takes 40 steps to climb up the moving up escalator respectively?

(1) 80 (2) 90(3) 100 (4) None of these

(Q2) A can take 10 steps per second and B can take 7 steps per second. A mischievously starts climbing down an escalator that is moving upwards and at the same instant B starts climbing up the same escalator. They meet after 5 seconds. If the escalator works at a steady rate of 4 steps per second then how many steps are visible when the escalator is stopped?

(1) 90 (2) 80(3) 85 (4) None of these

(Q3) In the above question, if the escalator was shut off at the instant when A and B meet,both being on different steps with A located above B, then how many steps from the ground is the step on which B stands?

(1) 45 (2) 65(3) 75 (4) 55

- 1 Like 6Comments
- Q3. (4)55. 27 Feb.
- Q2. (3)85. 27 Feb.

Swapnil Jha
@swapnil4ever2u
1.8
k

Q2) 10*5 - 5*4 + 7*5 + 5*4 = 85 steps

Swapnil Jha
@swapnil4ever2u
1.8
k

Q1) let the speed of steps be x steps/sec

50+ 10x = 40 + (40/3)x

=> x = 3 steps/sec

therefore total steps = 50 + 10*3 = 80 steps

50+ 10x = 40 + (40/3)x

=> x = 3 steps/sec

therefore total steps = 50 + 10*3 = 80 steps

Escalators _/\_

(Q1) P and Q walk up a moving up escalator at constant speeds. For every 5 steps that P takes Q takes 3 steps. How many steps would each have to climb when the escalator is switched off, given that P takes 50 and Q takes 40 steps to climb up the moving up escalator respectively?

(1) 80 (2) 90(3) 100 (4) None of these

(Q2) A can take 10 steps per second and B can take 7 steps per second. A mischievously starts climbing down an escalator that is moving upwards and at the same instant B starts climbing up the same escalator. They meet after 5 seconds. If the escalator works at a steady rate of 4 steps per second then how many steps are visible when the escalator is stopped?

(1) 90 (2) 80(3) 85 (4) None of these

(Q3) In the above question, if the escalator was shut off at the instant when A and B meet,both being on different steps with A located above B, then how many steps from the ground is the step on which B stands?

(1) 45 (2) 65(3) 75 (4) 55

- 3Comments
- 80,85,55. 26 Feb.
- 80,85,55. 26 Feb.