671. Two natural numbers whose sum is 72 cannot be in the ratio:
A. 1:2
B. 3:5
C. 1:3
D. 3:4

Explanation:
72 should be divisible by addition of the above ratio.
Using trial and error method
For (a): – 1+2 = 3, 72 is divisible by 3
For (b): – 3+5 = 8, 72 is divisible by 8
For (a): – 1+3 = 4, 72 is divisible by 4
For (a): – 3+4 = 7, 72 is not divisible by 7
Therefore, the answer is option (d)

672. A journey of 750 km was covered partly by car(x km) and partly by train(y km). If the distance travelled by train was 150 km more than the distance travelled by car, find x:y.
A. 2:3
B. 3:2
C. 3:4
D. 4:3

Explanation:
x+y = 750 y-x = 150 Solving,
y = 450
x = 300 x:y = 300:450 = 2:3

673. p is 50% more than q. Find the ratio of p to q.
A. 3:2
B. 1:2
C. 1:5
D. 2:1

Explanation:
p = q+(50/100)q = 1.5q p:q = 1.5q:q = 1.5:1 = 3:2

674. The sum of squares of three numbers is 280. If the numbers are in the ratio 3:5:6, find the greatest number.
A. 8
B. 6
C. 12
D. 18

Explanation:
Let the numbers be 3x,5x and 6x. (3x)²+(5x)²+(6x)²=280 9x²+25x²+36x²=280 70x²=280 x²=4 x=2 The greatest number is 6x=12.

675. If a flat costs Rs.4500 per sq. ft, and a commercial space costs Rs.9500 per sq. ft, then what is the ratio of their areas if the total cost of both are the same?
A. 9:19
B. 19:9
C. 15:28
D. 28:15

Explanation:
Let A1 be the area of flat and A2 be that of the commercial space
Total cost = area * rate
Therefore, cost of flat = A1*4500 ; cost of commercial space = A2*9500
Both the above costs are same
A1*4500 = A2*9500
A1:A2 = 9500:4500 = 19:9

676. The sum of three numbers is 172. The ratio of the first and second numbers is 8:11. The ratio of the second and third is 5:7. Find the second number.
A. 44
B. 55
C. 66
D. 77

Explanation:
Let the numbers be a, b and c. a+b+c = 172 a:b = 8:11 b:c = 5:7 11a = 8b a = 8b/11 7b = 5c c = 7b/5 (8b/11)+b+(7b/5) = 172 40b+55b+77b = 172*55 172b = 172*55 b=55

677. 4 singers, 5 dancers and 3 comperes divide an amount of Rs.130000 among themselves such that 3 comperes get as much as 2 dancers and 3 dancers get as much as 2 singers. Find the amount received by a singer.
A. Rs.18000
B. Rs.13000
C. Rs.15000
D. Rs.10000

Explanation:
4S+5D+3C=130000 3C=2D 3D=2S S=3D/2 [4*(3D/2)]+5D+2D = 130000 6D+5D+2D = 130000 13D = 130000 D = Rs.10000 S=3D/2 = Rs.15000

678. The sum of cubes of two numbers is 280. If the numbers are in the ratio 2:3, find the smallest number.
A. 4
B. 6
C. 3
D. 2

Explanation:
Let the numbers be 2x and 3x. (2x)³+(3x)³=280 8x³+27x³=280 35x³=280 x³=8 x=2 The numbers are 4 and 6.

679. Find the value of x when y = 5, if x varies directly as 4y-1 and x = 14 when y = 2.
A. 38
B. 35
C. 10
D. 28

Explanation:
Let z = 4y-1
When x = 14, y = 2, z = (4*2) – 1 = 7
Now, x varies directly as z = 4y-1
When y = 5, z = (4*5) – 1 = 19
x 14 7
y – 19
Therefore, x = (14*19)/7 = 38

680. The number of seats available for Biology and Computer Science in a school is in the ratio 5:8. They are to be increased by 30% and 25% . Find the new ratio.
A. 6:10
B. 13:20
C. 3:4
D. 35:33

Explanation:
Let the number of seats be 5x and 8x. New ratio
= (1.3*5x):(1.25*8x)
= 6.5x:10x
= 13:20

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