LIC AAO | QUANT QUIZ - 14 | S W A G

Directions (Q. 1-10): Study the following information carefully and answer the given questions.

1. Pradeep and Kishan together can complete typing work a book of 1008 pages in 12 days working 7 hrs per day. Pradeep is 25% more efficient than Kishan. A page contains an average of 333 words, then how many words can Pradeep type in an hour.
(a)    2000 words/hr
(b)    2050 words/hr
(c)    2100 words/hr
(d)    2220 words/hr
(e)    None of these

(d) 2220 words/hr
EXPLANATION :-
The Ratio of Efficiency of Pradeep and Kishan = 125/100 = 5/4.
The number of pages that can be typed by Pradeep and Kishan together in 1 Hr= 1008/(12x7)= 12.
The Pages typed by Pradeep = 12x5/9 = 20/3 pages = 20*333/3 = 2220 words/hr.

Also, Using Traditional Approach for better understanding :-
Let Kishan’s efficiency be X /hr.
Pradeep’s Efficiency will be 1.25X/hr.
Pradeep + Kishan = (X+1.25X)= 2.25X
Time = 12x7 = 84Hrs.
Work = (1008x333) words.
Efficiency = 2.25X
Time = (1008x333)/2.25X = 84(given)
112x1332/84 = X
X= 1776 = Kishan’s Efficiency
Pradeep’e Efficiency = 1.25* (1776)= 2220 wrds/Hr.

2. Two trains, one from place A to B and another from B to A started simultaneously. After they meet they reach their destinations after 12.25hrs and 17.64 hrs respectively. The ratio of their speeds is.
(a)    5:4
(b)    4:5
(c)    7:6
(d)    6:5
(e)    None of these

(d) 6:5
EXPLANATION :-
Theorem:- If two Trains/persons start at the same time in opposite directions from two points and after passing each other they complete the journey in ‘a’ and ‘b’ hrs respectively. Then,
1st’s speed/ 2nd’s speed = vb/va
For Proof of Theorem Please refer M.Tyra Chapter Time and Distance.

Now, Acc to Question and Above theorem, we have
Ratio of their speeds as √17.64/√12.25 = 4.2/3.5 = 6/5.
√ is under root
 

3. The difference between the compound interest and simple interest on an amount of Rs. 46000 for 2 year is Rs. 73.6. What the rate of interest?
(a)    4.25
(b)    4
(c)    5
(d)    3.75
(e)    None of these

(b) 4
EXPLANATION :-
Sum= diff.(100/r)^2
== > 46000= 73.6x10000/r^2
== > r^2 = 736/46 = 16
== > r = 4

4.  A person sold a cycle for Rs.918 and got a percentage of profit equal to the (4/75)th of the cost price. What is the cost price??
(a)    Rs. 575.00
(b)    Rs. 918.00
(c)    Rs. 650.00
(d)    Rs. 675.00
(e)    Rs. 871.52

(d) Rs. 675
EXPLANATION :-
Let CP be X
Profit% = (4X/75)%.
Profit = X*(4X/75)*(1/100) = X^2/1875
Now, (X^2/1875)+X = 918
Solving this quadratic equation, we get
X= 675,-2550 (neglecting –ve value)
X= 675.

5. A sum of money amounts to Rs. 2380 in four years at simple interest. If the rate of interest be raised by 30%, the sum amounts to Rs. 2584 during the same period. What is the rate of interest ?
(a)    8%pa
(b)    10%pa
(c)    12%pa
(d)    13%pa
(e)    Cannot be determined.

EXPLANATION :-
Let the sum be X and Rate of interest be r% pa
== > 2380-X = X*r*4/100…(i)
Also, 2584-X = X*1.3r*4/100…(ii)
2380-X/2584-X = 1/1.3
== > 3094-1.3X = 2584-X
== > 510= 0.3X = = > X= 1700
== > 2380-1700 = 1700*r*4/100
== > r = 680/68 = 10%pa

6. The compound interest on a certain sum of money for 2 years at 11% p.a is Rs. 16247. What will be the simple interest at the same rate and for same period ?
(a)    Rs. 14800
(b)    Rs. 15200
(c)    Rs. 15400
(d)    Rs. 15600
(e)    None of these

(c) Rs. 15400
EXPLANATION :-
16247 = P(1+11/100)^2 – P
== > 2321P = 16247*10000
== > P = 70000
SI = 70000x11x2/100 = 15400

7. 1677 litres of a mixture contains milk and water in the ratio 9 : 4. How much water is to be added to get a new mixture containing milk and water in the ratio 9 : 7 ?
(a)    312 litres
(b)    334 litres
(c)    348 litres
(d)    387 litres
(e)    396 litres

(d) 387 litres
EXPLANATION :-
Milk = 1677x9/(9+4)= 129*9 = 1161litres
Water = 1677-1161 = 516 litres.
Let the added water be X litres
1161/(516+X) = 9/7
== > 9X+4644 = 8127
== > X= 3483/9 = 387 litres.


8. Twelve years ago a father was 6 times as old as his son. After twelve years he will be 2.25 times as old as his son. What is the present age of father ?
(a)    48 years
(b)    52 years
(c)    60 years
(d)    72 years
(e)    80 years

(c) 60 years
EXPLANATION :-
Let the age of Son 12 years ago be X, So age of Father = 6X
After 12 yrs age of Son = X+12+12 = X+24 and Father = 6X+24.
6X+24/X+24 = 2.25 = 9/4
== > 24X+96 = 9X+216
== > 15X= 120 or X= 8
Present Age of Father = 6X+12 = 48+12 = 60.

9. How many three letter words, can be formed out of the letters of the word "SIDHANT", if repetition of letters is not allowed ?
(a)    5040
(b)    2520
(c)    840
(d)    420
(e)    210

(e) 210
EXPLANATION :-
Number of words = 7P3 = 7!/(7-3)! = 7!/4! = 7x6x5 = 210

10. A person sold a ball and a bat together for Rs.1966 there by making a profit of 16% on ball and 12% on bat. By selling them together for Rs.2024, he would have made a profit of 12% on ball and 16% on bat. What is the cost price of ball and bat together ?
(a)    1600
(b)    1650
(c)    1700
(d)    1750
(e)    1800

(d) 1750
EXPLANATION :-
1.16X + 1.12Y = 1966
1.12X + 1.16Y = 2024
Solving both we get X= 150, Y = 1600
X+Y = 1750