# 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 childrenâ€™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 Rohitâ€™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 â‰¥ y

c) If x < y

d) If x â‰¤ y

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

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

II) y13 â€“ (1259/2 / âˆšy) = 0

5) I) 9x2 + 198x â€“ 432 = 0

II) 7y2 + 14y â€“ 156 = 0

Directions (Q. 6 â€“ 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 % – –

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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 %

LCM of 16 and 20 = 80 units

(A + B)â€™s one day work = 5 units

(B + C)â€™s one day work = 4 units

Aâ€™s 6 days work + Bâ€™s 9 days work + Câ€™s 22 days work = 80

(A + B)â€™s 6 days work + (B + C)â€™s 3 days work + Câ€™s 19 days work = 80

(5*6) + (4*3) + Câ€™s 19 days work = 80

Câ€™s 19 days work = 80 â€“ 30 â€“ 12 = 38

Câ€™s one day work = 38/19 = 2 units

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

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 years ago, Rohit â€“ Agila = 12

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

Present age of Rohit and Agila = 7x â€“ 9, 4x â€“ 9

According to the question,

7x â€“ 4x = 12

3x = 12

X = 4

Present age of Rohit = 7x â€“ 9 = 19

Present age of Rohitâ€™s mother = 19 + 25 = 44 years

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

x2 â€“ (âˆš5 + 5) x + 5âˆš5 = 0

x2 – âˆš5x â€“ 5x + 5âˆš5 = 0

x (x – âˆš5) â€“ 5 (x – âˆš5) = 0

(x â€“ 5) (x – âˆš5) = 0

x = 5, âˆš5

II) y13 â€“ (1259/2 / âˆšy) = 0

y13 * y1/2 = 1259/2

y(13 + Â½) = (53)9/2

y27/2 = 527/2

y = 5

x â‰¤ y

I) 9x2 + 198x â€“ 432 = 0

9x2 + 216x â€“ 18x â€“ 432 = 0

9x (x + 24) â€“ 18 (x + 24) = 0

(9x â€“ 18) (x + 24) = 0

x = 2, -24

II) 7y2 + 14y â€“ 156 = 0

7y2 + 42y â€“ 26y â€“ 156 = 0

7y (y + 6) â€“ 26 (y + 6) = 0

(7y â€“ 26) (y + 6) = 0

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

Canâ€™t be determined

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 â€“ 33000 = Rs. 200

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

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 â€“ 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 â€“ 28500)/30000]*100 = 5 %

Required ratio = 8 : 5

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

The profit of item Q = 13500 â€“ 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

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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