Question

The ratio of Raj's age to Jennifer's age is now 7 : 4. 34 years ago, the
ratio was 6 : 1. How old is Raj now?

Raj is

years old now.

Recommended heuristic: Before and After Concept

Answer 1

The ratio of Raj's age to Jennifer's age is now 7 : 4.

Step 1: Write the ratio for after.

12 years ago, the ratio was 6 : 1. How old is Raj now?

Step 2: Write the ratio for before.

Age difference remains constant no matter what age each of them is at.

Step 3: Write the difference in the number of units for both ratios and make them the same.
The lowest common multiple of 3 and 5 is 15.

Step 4: Find 1 unit. Raj's age increases by 34, the number of units increases by 17 units.
35 units - 18 units = 17 units
17 units -> 34
1 unit -> 34 + 17 = 2

Step 5: Find Raj's age now, 35 units.
35 units ->35 × 2 = 70

Raj is 70 years old now.

Answer 2

Let Raj's current age = 7x and Jennifer's = 4x. 34 years ago their ages were 7x − 34 and 4x − 34, and the ratio then was 6:1:

(7x − 34)/(4x − 34) = 6
7x − 34 = 6(4x − 34) = 24x − 204
170 = 17x → x = 10

Raj's current age = 7x = 70 years.