# Problems on Numbers Quiz Set 003

### Question 1

If \${13/20}\$ of a number is 23, what is \$1{10/13}\$ of that number?

A

\$62{102/169}\$.

B

\$63{55/56}\$.

C

\$60{151/171}\$.

D

\$64{143/171}\$.

Soln.
Ans: a

Let the number be N. Then it is given that \${13/20}\$ x N = 23. ⇒ N = 23 X \${20/13}\$. ⇒ \${23/13}\$ x N = \${23/13}\$ x 23 X \${20/13}\$ = \${10580/169}\$.

\${23/13}\$ is same as \$1{10/13}\$. \${10580/169}\$ is same as \$62{102/169}\$.

### Question 2

A number is multiplied by 6, then 21 is added to it. The result remains the same if 13 is multiplied to the number and then 84 subtracted. What is the number?

A

15.

B

16.

C

14.

D

17.

Soln.
Ans: a

Let the number be n. From the given conditions we have \$6n + 21 = 13n - 84\$. Rearranging we have \$84 + 21 = 13n - 6n\$, ⇒ \$n = {84 + 21}/{13 - 6}\$. So n = 15.

### Question 3

What is 0.94949494...?

A

\$94/99\$.

B

\$95/99\$.

C

\$94/100\$.

D

\$94/101\$.

Soln.
Ans: a

0.94949494... is same as \$0.\ov 94\$. Let y = \$0.\ov 94\$. Multiply by 100, 100y = 94 + \$0.\ov 94\$ which is same as 94 + y. So 99y = 94, ⇒ y = \$94/99\$. So answer = \${94/99}\$.

### Question 4

What is 0.67676767...?

A

\$67/99\$.

B

\$68/99\$.

C

\$67/100\$.

D

\$67/101\$.

Soln.
Ans: a

0.67676767... is same as \$0.\ov 67\$. Let y = \$0.\ov 67\$. Multiply by 100, 100y = 67 + \$0.\ov 67\$ which is same as 67 + y. So 99y = 67, ⇒ y = \$67/99\$. So answer = \${67/99}\$.

### Question 5

What is x in \$3{113/x}\$ × \$3{1/13}\$ = \$11{5/7}\$?

A

140.

B

141.

C

139.

D

142.

Soln.
Ans: a

We can see that \$3{113/x}\$ = \${82/7}\$ × \${13/40}\$. ⇒ \${3x + 113}/x\$ = \${533/140}\$ ⇒ x = 140.