Source: Safalta
a) 80 years
b) 96 years
c) 72 years
d) 76 years
Let the ages of A and B 4
years ago are 4x and 5x respectively.
According to the question
(5x+12)/( 4x+12) = 11/13
52x + 156 = 55x + 132
3x = 24
x= 8
Sum of their present age = 4x+4+5x+4 = 9 (8)+8 = 80
(2) If x is subtracted from each of 23, 39, 32 and 56, the number so obtained in this order are in proportion. What is the mean proportional between (x + 4) and (3x +1)?
a) 15
b) 10
c) 12
d) 14
Required proportion:
(23-x)/(39-x) = (32-x)/(56-x) --- (i)
y hit and trial, we can find that x=5
satisfies the eq. (i)
Mean proportion of (x+4) and (3x+1)
i.e. 9 and 16 is √9 × 16 = 12
(3) The prices of two articles are in the ratio 4 : 5. If the price of the first article is increased by x% and that of the other is decreased by 30% , then the new prices of A and B will be in the ratio 10 : 7. The value of x is :
a) 24.5
b) 22.5
c) 25
d) 20
Let the price of the articles are 400
and 500.
According to the question
[400*(100+x)/100]/500*(100-30)/100 = 10/7
⇒ 400+4x = 500
⇒ x = 25 %
(4) A sum of Rs. x is divided among A, B and C such that the ratio of shares of A and B is 7 : 12 and that of B and C is 8 : 5. If the difference in the shares of A and C is Rs. 214 , then the value of x is :
(a) 11556
(b) 11128
(c) 11770
(d) 11342
Given, A:B = 7:12 and B:C = 8:5
Balancing the ratio for B
A:B:C = 14:24:15
⇒ A’s share = 14 unit
B’s share = 24 unit
C’s share = 15 unit
According to the question
15-14) = 1 unit = 214
Sum (x) = 14+24+15 = 53 unit
= 53 × 214 = 11342
(5) What is the ratio of the mean proportional between 4.8 and 10.8 and the third proportional to 0.4 and 2.4?
(a) 2 : 1
(b) 3 : 2
(c) 1 : 2
(d) 2 : 3
(6) If a : b = 3 : 2 then (5a + 2b) : (3a + 4b) is equal to:
(a) 16 : 15
(b) 8 : 7
(c) 19 : 17
(d) 17 : 14
Given, a : b = 3 : 2
Let a = 3k and b = 2k
5a + 2b) : (3a + 4b) ⇒
{5(3k) + 2(2k)} : {3(3k)+4(2k)}
⇒ 19k : 17K
= > 19 : 17
(7) If a : b = 2 : 5 , c : b = 3 : 4 , then a : b : c is equal to :
(a) 6 : 15 : 20
(b) 8 : 20 : 15
(c) 2 : 5 : 4
(d) 2 : 5 : 3
(8) If (5a - 3b) : (4a - 2b) = 2:3, then a:b is equal to
(a)3:4
(b)2:3
(c) 5:7
(d) 7:5
(9) Two numbers are in the ratio 3:4. On increasing each of them by 30, the ratio becomes 9:10. The numbers are :
(a) 30,40
(b) 15,20
(c) 12,16
(d) 18,24
No. are 3K and 4K = 15, 20
(10) The ratio of incomes of A and B is 2 : 3 and that of their expenditure is 1 : 2. If 90% of B’s expenditure is equal to the income of A , then what is the ratio of the savings of A and B?
a) 1 : 1
b) 9 : 8
c) 8 : 7
d) 3 : 2