# Question

The number of local stamps in a collection was 2/3 of the total number of stamps. After 156 local stamps were added to the collection, the number of local stamps became 4/5 of the total number of stamps. How many stamps were there in the collection at first?

Method 1 :
local stamps ——- 2u
total stamps ——- 3u
(2u + 156)/(3u + 156) = 4/5
5 x (2u + 156) = 10u + 780 ——- 4 x (3u + 156) = 12u + 624
12u – 10u = 2u ——- 780 – 624 = 156
1u ——- 156/2 = 78
3u ——- 78 x 3 = 234

Method 2 :
Before —
local : non-local
2u : 1u

After —
local : non-local
4u : 1u

4u – 2u = 2u ——- 156
1u ——- 156/2 = 78
3u ——- 78 x 3 = 234

Ans : 234 stamps.
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I assume total stamps = local stamps + foreign stamps. Question completely left out on mentioning “foreign”.

Method 1: Model above

Method 2: Ratio

Local            Foreign              Total

Ratio at first           2u                    1u                     3u

Change             +156 stamps

Ratio at end            4u                    1u                     5u

Note there should be no change in foreign stamps. So keep at 1u before and after.

Looking at “local” column, 2u=156 –> u=78

Total at first = 3u = 234#

Method 3: Fractions

Same no. of foreign stamps,     1/3 Total Before = 1/5 Total After

Since numerator is the same, no extra work required. Total has increased by 2 units, from 3 units (Total Before) to 5 units (Total After) in denominator.

2u=156 –> u=78

Total at first = 3u = 234#

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