691. If the number obtained on interchanging the digits of a two-digit number is 18 more than the original number and the sum of the digits is 8, then what is the original number ?
A. 26
B. 35
C. 53
D. Cannot be determined

692. A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. The number is :_________?
A. 18
B. 24
C. 42
D. 81

693. Find the number which when multiplied by 15 is increased by 196.
A. 14
B. 20
C. 26
D. 28

Explanation:
Let the number be x. Then, 15x – x = 196
14x = 196 x = 14.

694. The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is :___________?
A. 20
B. 30
C. 40
D. None of these

695. Three numbers are in the ratio of 3 : 4 : 6 and their product is 1944. The largest of these numbers is :___________?
A. 6
B. 12
C. 18
D. None of these

Explanation:
Let the numbers be 3x, 4x and 6x.
Then, 3x x 4x x 6x = 1944 72×3 = 1944
x3 = 27 ,=> x = 3
∴ Largest number = 6x = 18,

696. If the sum of a number and its square is 182, what is the number ?
A. 15
B. 26
C. 28
D. 13

Explanation:
Let the number be x.
Then, x + x2 = 182 x2 + x – 182 = 0
(x + 14) (x – 13) = 0 x = 13.

697. The sum of two numbers is 25 and their difference is 13. Find their product :
A. 104
B. 114
C. 315
D. 325

Explanation:
Let the numbers be x and y. Then, x + y = 25 and x – y = 13.
4xy = (x + y)2 – (x – y)2 = (25)2 – (13)2 = 625- 169 = 456
=> xy = 114.

698. If the sum of two numbers is 33 and their difference is 15, the smaller number is :__________?
A. 9
B. 12
C. 15
D. 18

Explanation:
Let the numbers be x and y.
Then, x + y = 33 …(i)
and x – y = 15 …(ii)
Solving (i) and (ii), we get : x = 24, y = 9.
∴ Smaller number = 9.

699. A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office?
A. 3 km
B. 4 km
C. 5 km
D. 6 km

700. A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.
A. 121 km
B. 242 km
C. 224 km
D. 112 km

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