Arithmetic

Ratio, Proportion & Variation

Medium

One-half of a certain number is equal to 65% of the second number. What is the ratio of the first number to second number?

13:10

8:13

13:8

10:13

✅ Correct Option: 1

Let the first number = $x$

Let the second number = $y$

One-half of the first number equals 65% of the second number:

$\frac{x}{2} = 65\% \text{ of } y$

$\frac{x}{2} = \frac{65}{100} \times y$

Simplifying $\frac{65}{100}$ :

$\frac{65}{100} = \frac{13}{20}$

So:

$\frac{x}{2} = \frac{13}{20} \times y$

Multiply both sides by 2:

$x = 2 \times \frac{13}{20} \times y$

$x = \frac{26}{20} \times y$

$x = \frac{13}{10} \times y$

Finding the ratio:

$\frac{x}{y} = \frac{13}{10}$

Therefore, the ratio of the first number to the second number is $13:10$ .

2023: 21 May Shift 1

The ratio of ages of 2 boys is 3:7. After 2 years, the ratio of their ages will become 5:9. The ratio of their ages after 10 years will be

2022: 8 Aug Shift 1

Ratio between age of P and Q is 5 : 7. If 2 years ago Q's age was 2 years more than the age of P after 4 years, then find their total age

2022: 20 Aug Shift 1

Sum of two numbers is 44 and their difference is 16. The ratio of these number is :

2025: 14 May Shift 1

Two numbers a and b are in the ratio 3:2 and their sum is 25. The value of a is?

2026: 19 May Shift 2

IF A : B = $\frac{2}{9}$ : $\frac{1}{6}$ , B : C = $\frac{2}{7}$ : $\frac{5}{21}$ and D : C = $\frac{7}{10}$ : $\frac{3}{5}$ , D : E = $\frac{5}{7}$ : $\frac{3}{14}$

then

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	C : A	I.	32 : 7
B.	D : B	II.	24 : 7
C.	B : E	III.	35 : 36
D.	A : E	IV.	5 : 8

Choose the correct answer from the options given below:

2026: 25 May Shift 1

If 7 : x = 17.5 : 22.5, then find the value of x.

One-half of a certain number is equal to 65% of the second number. What is the ratio of the first number to second number?

Solution

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