Q1.
For each district, find out if the number of certificates were sufficient? If insufficient, calculate how many certificates fell short. If extra, calculate how many certificates were in excess. Chittoor, A.P. — printed 18,225, attended 18,104. Jaunpur, U.P. — printed 19,043, attended 19,265. Raigad, Maharashtra — printed 20,863, attended 19,974.
Answer
Chittoor and Raigad had enough certificates. Jaunpur fell short by 222.
| District | Printed | Attended | Enough? | Short / Extra |
|---|---|---|---|---|
| Chittoor, A.P. | 18,225 | 18,104 | Yes | 121 extra |
| Jaunpur, U.P. | 19,043 | 19,265 | No | 222 short |
| Raigad, Maharashtra | 20,863 | 19,974 | Yes | 889 extra |
Step 1 — compare the two numbers for each district. If the printed number is bigger, there are certificates to spare. If it is smaller, some students will not get one.
Chittoor — 121 certificates in excess
- 18,225 printed is more than 18,104 attended, so there are enough.
- Ones: 5 − 4 = 1. Tens: 2 − 0 = 2. Hundreds: 2 − 1 = 1. Thousands: 8 − 8 = 0. Ten-thousands: 1 − 1 = 0. No regrouping is needed anywhere.
- 18,225 − 18,104 = 121.
Jaunpur — 222 certificates short
- 19,043 printed is less than 19,265 attended, so there are not enough.
- Take the smaller from the bigger to find the shortfall.
- Ones: 5 − 3 = 2. Tens: 6 − 4 = 2. Hundreds: 2 − 0 = 2. Thousands: 9 − 9 = 0. Ten-thousands: 1 − 1 = 0.
- 19,265 − 19,043 = 222.
Raigad — 889 certificates in excess
- 20,863 printed is more than 19,974 attended, so there are enough.
- Ones: 3 is smaller than 4. Take 1 ten from the 6 tens. Ones become 13, tens become 5. 13 − 4 = 9.
- Tens: 5 is smaller than 7. Take 1 hundred from the 8 hundreds. Tens become 15, hundreds become 7. 15 − 7 = 8.
- Hundreds: 7 is smaller than 9. Take 1 thousand from the 0 thousands — but there are none, so first take 1 ten-thousand from the 2 and turn it into 10 thousands. Now thousands are 10; take 1 of them for the hundreds. Hundreds become 17, thousands become 9, ten-thousands become 1. 17 − 9 = 8.
- Thousands: 9 − 9 = 0. Ten-thousands: 1 − 1 = 0.
- 20,863 − 19,974 = 889.
Check them all: 18,104 + 121 = 18,225 ✓ 19,043 + 222 = 19,265 ✓ 19,974 + 889 = 20,863 ✓