High Level Maths Quiz: Part 8

Directions:  In the following questions, two statements numbered I and II are given, on solving them, we get quantities I and II respectively.c ompare both the quantities and choose the correct option.

Question 1:

Quantity I: A person saves every year 10% of his income , if his income increases every year by 5% then his savings increase every year by ?
Quantity II: The salary of a worker is first increased by 50% and afterwards reduced by 50%.What is net change in his salary ?


(a) quantity I > quantity II

(b) quantity I < quantity II
(c) quantity I ≥ quantity II 

(d) quantity I ≤ quantity II
(e) quantity I =quantity II or relation cannot be determined

Question 2:

Quantity I: ‘A” invests Rs. 6000 for 12 months in a business , how much ‘B’ should invest in order that the profit after 1 year may be divided into the ratio of 2:3 ?
Quantity II: Three partners invest Rs. 3000 , Rs.3500 and Rs. 1500 in a business. They divide Rs. 1200 as a profit. What is the share of the second partner?

(a) quantity I < quantity II 

(b)quantity I > quantity II
(c) quantity I ≤ quantity II 

(d)quantity I ≥ quantity II
(e) quantity I =quantity II or relation cannot be determined

Question 3:

Quantity I: Ten years ago A was half of B in age. If the ratio of their present ages is2:#.waht will be the total of their present ages ?
Quantity II: The sum of the ages of a father and a son is 60 years. Also, 5 years ago , the fathers age was 9 times the age of the son .The present age of the father is ?

(a) quantity I < quantity II 

(b)quantity I > quantity II
(c) quantity I ≤ quantity II (d)quantity I ≥ quantity II
(e) quantity I =quantity II or relation cannot be determined

Question 4:

Quantity I: 1 man or 2 women or 3 boys can do a piece of work in 88 days .1 man , 1woman and 1boy will do it in ?
Quantity II: A and B can do a piece of work in 18 days .B and C together can do it in24 days. If A is twice as good a work man as C , find in what time B alone can do it ?

(a) quantity I < quantity II 

(b) quantity I ≤ quantity II
(c) quantity I > quantity II 

(d) quantity I ≥ quantity II
(e) quantity I =quantity II or relation cannot be determined

Question 5:

Quantity I: A trader lists his article at 15% above cost price and allows a discount of 5% on cash payment. Find his profit per cent.
Quantity II: A dealer marks his goods 25% above the cost price. He then allows some discount on it and makes a profit of 10%. Find the rate of discount.

(a) quantity I < quantity II 

(b)quantity I > quantity II
(c) quantity I ≤ quantity II 

(d)quantity I ≥ quantity II
(e) quantity I =quantity II or relation cannot be determined

Solution

Solution (1) 

Quantity I:

let the income in any year be x
So that saving for that year be 10% of x
New income = 105% x
New saving = 10% of 105% of x  = 10.5% of x
Increase = 0.5% of x

Quantity II

Percentage increase = 0.5 / 10 * 100 % = 5%
A decrease of 50 % of 50 = 25%
Hence (b) quantity II > quantity I

Solution (2) 

Quantity I

6000 * 12 / (x * 12 ) = 2/3
24x = 216000
X= Rs. 9000

Quantity II

3000:3500 :1500
i.e. 6: 7: 3
share of second partner = 7/16 *1200 =Rs,.525
So quantity I > quantity II.

Hence (b) is the right answer

Solution (3) 

Quantity I: 

Let A’s age 10 years ago = x years
Then B’s age 10 years ago = 2x years
According to the question
X+10 / 2x +10 = 2/3
3 (x+10 ) = 2(2x + 10)
3x +30 = 4x + 20
X= 10
Total of their present ages = x+10 +2x+10 = 50
Quantity II : F+S = 60 ……… ( 1)
F -5 = 9(S-5)
F-5 = 9S-45
F-9S = -40………. (2)

SUB (1) AND (2) , WE GET

10S = 100
S = 10
Age of father = 60 – S = 50 Years
Hence (e) is the correct answer

Solution (4) 

Quantity I: 

1man = 2 women = 3 boys
1 woman = ½ man
1 boy = 1/3 man
1man + 1 woman +1boy
= 1+1/2 + 1/3 = 11/6 men
Now, 1 man do the work in 88 days
11/6 men can do it in 88 days * 6/11= 48 days

Quantity II: 

A’s 1 day work = C’s one day work
(A+B )’s 1 day work = (B’s one day work ) + C ‘s one day work
(or)
(B’s 1days work ) + (C’s 1 day work ) = 1/18
But (B’s 1 days work ) + (C’s 1days work ) = 1/24
C’s 1day’s work = 1/18 – 1/24 = 1/72
B’s one day work will be 1/ 36
Hence B alone can finish the work in 36days
ANSWER: (c ) So quantity I > quantity II

Solution (5) 

Quantity I: 

Let the CP be rs.100
Then MP = 115 and d = 5%
SP = 100-d% / 100 * MP
SP = 10925
Profit per cent = 9.25%
Quantity II: Let the CP be Rs.100 Then MP = 125
And SP = (110 /100 * 100 )
Rate of discount = (15/125*100 ) % = 12%
Hence (a) quantity II > quantity I