Quantitative Techniques Test Paper for CLAT 2020

Quantitative Techniques Test Paper for CLAT 2020

Question 1:​​ In SBI 2015 exam, from State P 8% of the total appeared candidates got selected and the same number of candidates appeared from State Q. Out of appeared candidates, 9% of candidates got selected and that is 50 more than selected candidates from State P. While From State R the number of candidates that got selected is 50 more than State Q which is 5% of the total appeared candidates.

• • What was the number of candidates that appeared in state P and Q?

• 5200 (b)​​ 5000​​  (c)​​ 5500​​  (d)​​ 5250​​ 

• • If the number of appeared candidates increased by 10% in State P in 2016 ​​ then how many candidates would be expected to be selected in the same state in 2016 if the percentage of selection is the same as 2015?

• 400  (b)​​ 440  (c)​​ 450  (d)​​ 500

• • What is the number of selected candidates in State R?

• 500​​  (b)​​ 450​​   (c)​​ 440​​   (d)​​ 400

• • How many candidates appear in the exam in state R?

• 5000 (b)​​ 1000 (c)​​ 10000 (d)​​ 7500

• • If the number of appeared candidates increased by 10% in State Q in 2016 ​​ then how many candidates would be expected to be selected the State R in 2016 if the percentage of selection​​ in State Q​​ is the same as 2015​​ with all other conditions as in the question?

• 540​​  (b)​​ 500 ​​  (c)​​ 545​​   (d)​​ 550

Question 2:In purchasing an item_1 costing Rs. 800, Sneha paid a tax of 9% while purchasing another item_2 costing Rs. 5000 she paid the tax of 12%. She resells item_1 at Rs. 900 and item_2 at Rs. 5454​​ at a discount of 10% for both items.​​ 

2.1​​  How much tax did Sneha paid while buying both the items?

 (a)​​ 672​​   (b)​​ 650​​   (c)​​ 642  (d)​​ 662 

2.2​​  Which of the following statements is true?

 (a)​​ loss of 3.2%(item_1) and Profit of 2.1%(item_2)

 (b)​​ loss of 2.2%(item_1) and Profit of 3.1%(item_2)

​​  (c)​​ profit of 3.2%(item_1) and Profit of 2.1%(item_2)

 (d)​​ profit of 3.2%(item_1) and loss of 2.1%(item_2)

2.3​​  What was the profit/loss that Sneha incurred after selling both the items?

 (a)​​ loss of 228  (b)​​ profit of 322 

(c)​​ loss of 118  (d)​​ profit of 554  ​​​​ 

2.4. How much mark up did Sneha put on the second item she purchased?

 (a)​​ 21.2%​​  (b)​​ 10%​​  (c)​​ 22%​​  (d)​​ 8.2%

2.5​​  How much markup Sneha should have done to avoid loss?​​ 

 (a)​​ 11.12% (b)​​ 12%  (c)​​ 10%  (d)​​ 15%

Answers and Solutions

• • Ans:​​ (b) 5000

Sol:​​ Let the number of candidates from State P that appeared in exam be x

Then, the number of candidates who got selected from state P = 8% of x = 0.08x  ​​ ​​ ​​​​ As the number of appeared candidates in Q = ​​ number of appeared candidates in P

  ​​ ​​ ​​​​ Number of appeared candidates from State Q = ​​ x

  ​​ ​​ ​​​​ Candidates selected from state Q = 9% of x = 0.09x

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ Also, selected candidates from Q = Selected candidates from P + 50​​ 

  0.09x = 0.08x + 50​​ 

  0.01x = 50

  X = 50/0.01 = 5000

• • Ans:​​ (b) 440

Sol:​​ As the number of appeared candidates in state P is 5000 from the previous question,

  ​​ ​​ ​​ ​​​​ In 2016, appeared candidates ​​ = 10% increase from 5000 = 1.1*5000 = 5500

  ​​ ​​ ​​ ​​​​ The same %age of candidates got selected in 2016 = 5500*0.08 = 440

• • Ans:​​ (a) 500

Sol:​​ As the selected candidates from R = Selected candidates in Q + 50

  ​​ ​​ ​​​​ Selected candidates from Q = 0.09x = 5000*0.09 = 450

  ​​ ​​ ​​​​ Selected candidates from Q = 450+50 = 500​​ 

• • Ans:​​ (c) 10000

Sol:​​ As the number of selected students is 500 which is 55 of appeared candidates,​​ 

  ​​ ​​ ​​​​ Appeared candidates = 500*100/5 = 10000

• • Ans:​​ (C) 545

Sol:​​ Increase in number of candidates is 10% of state Q, hence number of appeared candidates = 5000*1.1 = 5500

  ​​ ​​ ​​​​ Selected candidates from Q = 9% of 5500 = 495

  ​​ ​​ ​​​​ Selected candidates from R = Selected candidates from Q + 50 = 495+50 = 545

2.1 Ans: (a) 672

 ​​ ​​ ​​ ​​ ​​ ​​​​ SOL:​​ Tax on item_1 = 800*9/100 = 72

  ​​ ​​ ​​​​ Tax on item_2 = 5000*12/100 = 600

  ​​ ​​ ​​​​ Total Tax paid = 600+72 = 672

2.2 Ans:​​ (D) profit of 3.2%(item_1) and loss of 2.1%(item_2)

 ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ SOL:​​ SP of Item_1 = 900 while cost price = 800+72(tax is also a cost) = 872

  ​​ ​​ ​​ ​​ ​​​​ Profit = 900-872 = 28​​  Profit% = 28*100/872 = 3.2%​​ 

  ​​ ​​ ​​ ​​ ​​​​ SP of Item_2 = 5454 while CP = 5000+600(tax) = 5600

  ​​ ​​ ​​ ​​​​ Loss = 5600-5454 = 118 Loss% = 118*100/5600 = 2.1%

2.3 ANS: (C) loss of 118

 ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ SOL: Explained in previous part.

2.4 ANS: (d) 8.2%

 ​​ ​​ ​​ ​​ ​​ ​​​​ SOL:​​ SP of item_2 = 5454

  ​​ ​​ ​​ ​​ ​​​​ Discount of 10%, hence Marked price = 5454/0.9 = 6060

  ​​ ​​​​ Mark up = Marked price – CP /CP = (6060-5600)*100/5600 = 8.2%

2.5 ANS: (a) 11.2%

 ​​ ​​ ​​ ​​ ​​​​ Sol:​​ To avoid losses the SP must be equal to CP, if the same discount has to be given,​​ 

  ​​ ​​ ​​​​ Hence at SP = 5600 , Marked Price = 5600/0.9 = 6222.2

  ​​ ​​ ​​​​ Mark up = (6222-5600)*100/5600 = 11.2%