LIC AAO Mains Quantitative Aptitude Questions 2019 (Day-09)

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1) A and B together can complete the job in 16 days, B and C together can complete the job in 20 days. First A did the job for 6 days, B did the job for 9 days and C completed the remaining job in 22 days. Find the number of days in which C alone can complete the job?

a) 40 days

b) 48 days

c) 30 days

d) 36 days

e) None of these

2) Rajeev spent 15 % of his monthly salary on food, 20 % on children’s education, 10 % on insurance and X % on other expenses. If the difference between the amount spent on food and insurance is Rs. 4000 and the saving is Rs. 20000, then find the value of X?

a) 25 %

b) 20 %

c) 35 %

d) 30 %

e) None of these

3) The difference between the ages of Rohit and Agila, 3 years ago is 12 years. If the ratio of their ages, 9 years hence will be 7 : 4, then find the present age of Rohit’s mother, who is 25 years older than Rohit?

a) 34 years

b) 46 years

c) 38 years

d) 44 years

e) None of these

Directions (Q. 4 – 5) In the following questions, two equations I and II are given. You have to solve both the equations and give answer as,

a) If x > y

b) If x ≥ y

c) If x < y

d) If x ≤ y

e) If x = y or the relation cannot be established

4) I) x2 + 53/2 = (51/2 + 5) x

II) y13 – (1259/2 / √y) = 0

5) I) 9x2 + 198x – 432 = 0

II) 7y2 + 14y – 156 = 0

Directions (Q. 6 – 10): Study the following information carefully and answer the given questions.

The following table shows the Cost price, Selling price and marked price of 4 different items. Some values are missing here.

Items Cost price

(In Rs.)

Marked price (In Rs.) Profit % Profit

(In Rs.)

Selling price (In Rs.)
P 20000 3000
Q 15000 25 % 13500
R 18000 20 % 2640
S 22800 25 %

 

6) Find the difference between the cost price of item P and R together to that of the marked price of item Q and R together, if the discount % given by the shopkeeper for item R is 12 %?

a) Rs. 500

b) Rs. 600

c) Rs. 400

d) Rs. 200

e) None of these

7) Find the average selling price of all the given items together, if the discount % given by the shopkeeper for item R is 12 %?

a) Rs. 20210

b) Rs. 22560

c) Rs. 24470

d) Rs. 19820

e) None of these

8) Find the ratio between the discount % given by the shopkeeper for item P to that of item S, the marked price of item P and item S is Rs. 25000 and Rs. 30000 respectively?

a) 11 : 7

b) 13 : 9

c) 8 : 5

d) 22 : 15

e) None of these

9) The total profit earned by the item P and Q together is approximately what percentage of total profit earned by the item R and S together?

a) 77 : 128

b) 95 : 139

c) 149 : 162

d) 273 : 316

e) None of these

10) The marked price of item P and S together is approximately what percentage of selling price of item Q and R together, if the discount % given to the item P and S is 8 % and 5 % respectively and the cost price of item R is Rs. 13200?

a) 175 %

b) 160 %

c) 135 %

d) 190 %

e) 220 %

Answers :

1) Answer: a)

LCM of 16 and 20 = 80 units

(A + B)’s one day work = 5 units

(B + C)’s one day work = 4 units

A’s 6 days work + B’s 9 days work + C’s 22 days work = 80

(A + B)’s 6 days work + (B + C)’s 3 days work + C’s 19 days work = 80

(5*6) + (4*3) + C’s 19 days work = 80

C’s 19 days work = 80 – 30 – 12 = 38

C’s one day work = 38/19 = 2 units

C alone can complete the work in, (80/2) = 40 days

2) Answer: d)

According to the question,

(15 % – 10 %) of salary = 4000

5 % of salary = 4000

Total salary = 4000*(100/5) = Rs. 80000 = 100 %

Savings % = (20000/80000)*100 = 25 %

Total salary (100 %) = Expense (75 %) + Savings (25 %)

75 % = (15 % + 20 % + 10 % + X %)

X % = 75 % – 45 % = 30 %

3) Answer: d)

3 years ago, Rohit – Agila = 12

9 years hence, The ratio of Rohit and Agila = 7 : 4 (7x, 4x)

Present age of Rohit and Agila = 7x – 9, 4x – 9

According to the question,

7x – 4x = 12

3x = 12

X = 4

Present age of Rohit = 7x – 9 = 19

Present age of Rohit’s mother = 19 + 25 = 44 years

4) Answer: d)

I) x2 + 53/2 = (51/2 + 5) x

x2 – (√5 + 5) x + 5√5 = 0

x2 – √5x – 5x + 5√5 = 0

x (x – √5) – 5 (x – √5) = 0

(x – 5) (x – √5) = 0

x = 5, √5

II) y13 – (1259/2 / √y) = 0

y13 * y1/2 = 1259/2

y(13 + ½) = (53)9/2

y27/2 = 527/2

y = 5

x ≤ y

5) Answer: e)

I) 9x2 + 198x – 432 = 0

9x2 + 216x – 18x – 432 = 0

9x (x + 24) – 18 (x + 24) = 0

(9x – 18) (x + 24) = 0

x = 2, -24

II) 7y2 + 14y – 156 = 0

7y2 + 42y – 26y – 156 = 0

7y (y + 6) – 26 (y + 6) = 0

(7y – 26) (y + 6) = 0

y = 26/7, -6 = 3.71, -6

Can’t be determined

6) Answer: d)

The selling price of item R = 18000*(88/100) = Rs. 15840

The cost price of item R = 15840*(100/120) = Rs. 13200

The cost price of item P and R together

= > 20000 + 13200 = Rs. 33200

The marked price of item Q and R together

= > 15000 + 18000 = Rs. 33000

Required difference = 33200 – 33000 = Rs. 200

7) Answer: a)

The average selling price of all the given items together

= > [(20000 + 3000) + 13500 + (18000*(88/100)) + (22800*(125/100)]/4

= > [23000 + 13500 + 15840 + 28500]/4

= > 80840/4 = Rs. 20210

8) Answer: c)

The selling price of item P = 20000 + 3000 = Rs. 23000

The marked price of item P = Rs. 25000

The discount % given by the shopkeeper for item P

= > [(25000 – 23000)/25000]*100 = 8 %

The selling price of item R = 22800*(125/100) = Rs. 28500

The marked price of item R = Rs. 30000

The discount % given by the shopkeeper for item R

= > [(30000 – 28500)/30000]*100 = 5 %

Required ratio = 8 : 5

9) Answer: b)

The cost price of item Q = 13500*(100/125) = Rs. 10800

The profit of item Q = 13500 – 10800 = Rs. 2700

The total profit earned by the item P and Q together

= > 3000 + 2700 = Rs. 5700

The total profit earned by the item R and S together

= > 2640 + (22800*(25/100))

= > 2640 + 5700 = Rs. 8340

Required ratio = 5700 : 8340 = 95 : 139

10) Answer: d)

The marked price of item P and S together

= > 23000*(100/92) + 22800*(125/100)*(100/95)

= > 25000 + 30000 = Rs. 55000

The selling price of item Q and R together

= > 13500 + (13200 + 2640) = Rs. 29340

Required % = (55000/29340)*100 = 187.45 % = 190 %

 

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