Arithmetic - Percentage - Previous Year CAT/MBA Questions

Answer: Option A

Text Explanation :

Let the total matches played so far = m.
Number of matches won = 0.4m

After playing n more matches and winning all the matches, win rate becomes 50%.
Total matches played = m + n
Total matches won = 0.4m + n​​​​​​​
⇒ 0.4m + n = 50% of (m + n)
⇒ 0.4m + n = 0.5m + 0.5n
⇒ 0.5n = 0.1m
⇒ m : n = 5 : 1
⇒ m = 5x and n = x   ...(1)

After playing 15 more matches and winning all the matches, win rate becomes 60%
Total matches played = m + n + 15
Total matches won = 0.4m + n​​​​​​​ + 15
⇒ 0.4m + n + 15 = 60% of (m + n + 15)
⇒ 0.4m + n + 15 = 0.6m + 0.6n + 9
⇒ 0.4n + 6 = 0.2m
⇒ 0.4 × x + 6 = 0.2 × 5x
⇒ 0.4x + 6 = x
⇒ x = 10

∴ Matches played by Guava club so far = m = 5x = 50.

Hence, option (a).

Answer: Option A

Text Explanation :

Total percentage incentive when number of team members = 1 = 100%
Total percentage incentive when the number of team members = 2 =160%
Total percentage incentive when the number of team members = 3=180%
Total percentage incentive when the number of team members = 4= 190%
Total percentage incentive when the number of team members >4 = 200%
From 1, Number of people in 8 different projects = 6, 3, 3, 3, 3, 2, 2, 2 respectively
From 2, Given, exactly three projects are rated C and 4.8 lakh is paid in total
A minimum of 3 lakhs has to be paid for rating C => 3 *1.6 = 4.8lakhs ⇒ All 2 member teams have been rated C
From 3, one project has been rated A*. Let that project be handled by the team of 3 members ⇒ Incentives = 180% of 6 = 10.8 lakh
Now remaining 6, 3, 3, 3 should be either rated A or B and the total incentives should be equal to 45 - 10.8 - 4.8 = 29.4 lakhs
Let us assume 6 has been rated B ⇒ Incentives = 200% of 3 = 6 lakhs
The remaining 23.4 lakhs should come from 180% $\frac{23.4}{1.8}$ = 13 lakhs

Hence the remaining 3,3,3 can be rated as A, A, B
Hence final ratings are and total payouts are
6 - B - 6lakhs
3- A - 9 lakhs
3-A - 9 lakhs
3-B - 5.4 lakhs
3-A* - 10.8lakhs
2-C - 1.6 lakhs
2-C - 1.6 lakhs
2-C - 1.6 lakhs

Answer: Option B

Text Explanation :

Number of messages send by Bina = 30% of 600 = 180
Number of messages send by Divya = 20% of 600 = 120

Remaining messages (300) are sent by Anita and Chitra equally i.e., Anita and Chitra sent 150 messages each.

Jokes sent by Anita = 60% of 150 = 90
Jokes sent by Bina = 40% of 180 = 72
Jokes sent by Chitra = 80% of 150 = 120
Jokes sent by Divya = 50% of 120 = 60

Total Jokes sent = 90 + 72 + 120 + 60 = 342

∴ Percentage of jokes that were neither sent by Bina or Divya = 210/342 × 100 = 61.4%

Hence, option (b).

Answer: Option A

Text Explanation :

Since final salary for all five employees is same, least hike will be for that employee who has the highest initial salary.

Again, since final salary for all five employees is same, initial salary will be highest for that employee who has least overall % change.

Let us calculate % change for all the employees.

We know when a number is successively increased b a% and then b%, overall % change is a + b + ab/100.

Here let us assume the value of p as 10%

Therefore, % change for 

A: 10 + 11 + 10 × 11/100 = 21 + 1.1 = 22.1%

B: 12 + 9 + 12 × 9/100 = 21 + 1.08 = 22.08%

C: 13 + 8 + 13 × 8/100 = 21 + 1.04 = 22.04%

D: 14 + 7 + 14 × 7/100 = 21 + 0.98 = 21.98%

E: 15 + 6 + 15 × 6/100 = 21 + 0.90 = 21.90%

∴ Least % change is for E, hence E has the highest initial salary hence the least hike.

Hence, option (a).

Answer: Option D

Text Explanation :

Given, $P\left(1+\frac{X}{100}\right)\left(1-\frac{Y}{100}\right)$ = P

⇒ $\left(1+\frac{X}{100}\right)\left(1-\frac{Y}{100}\right)$ = 1   …(1)

⇒ X > Y
 
It is also given that X – Y = Y.

⇒ X = 2Y

Substituting this in (1)

⇒ $\left(1+\frac{2Y}{100}\right)\left(1-\frac{Y}{100}\right)$ = 1

⇒ 1 -  ($\frac{2Y^2}{10000}$ + $\frac{Y}{100}$ = 1

⇒ Y = 50

∴ X = 100

Hence, option (d).

Answer: Option A

Text Explanation :

​​​​​​​

Total tax will be minimum if income of 5 persons is not more than 500 and income of 4 persons is minimum and also in the range (500, 2000]. Total tax will be maximum if income of 5 persons is maximum possible and income of 4 persons is maximum in the range (2000, 5000].

Minimum tax > (5 × 0) + (4 × 0) + (3 × 75) + (3 × 375) = Rs. 1350

Maximum tax range < (3 × 0) + (3 × 75) + (4 × 375) + (5 × 1125) = Rs. 7350

Hence, option (a).

Answer: Option E

Text Explanation :

Let T, M, G, L and B be the capacities of Tina’s, Mina’s, Gina’s, Lina’s and Bina’s bucket.

Hence, T > M > G > L > B

Assume that they spill x litres of water.

Hence, the percentages of the water spilled by them are;

(x/T) × 100, (x/M) × 100, (x/G) × 100, (x/L) × 100 and (x/B) × 100 respectively.

As, , T > M > G > L > B, this implies that x/ T < x/M < x/G < x/L < x/B

Hence, percentage of water spilled is highest for Bina.

Hence, option (e).