Gate Mock Test, Gate Practice Test question, Answer carefully with all clear steps and accuracy with given answer:
In appreciation of the social improvements completed in a town, a wealthy philanthro

Question

Gate Mock Test, Gate Practice Test question, Answer carefully with all clear steps and accuracy with given answer:
In appreciation of the social improvements completed in a town, a wealthy philanthropist decided to gift Rs 750 to each male senior citizen in the town and Rs 1000 to each female senior citizen. Altogether, there were 300 senior citizens eligible for this gift. However, only 8/9
t
h
th
  of the eligible men and 2/3
r
d
rd
  of the eligible women claimed the gift. How much money (in Rupees) did the philanthropist give away in total?

1,50,000

2,00,000

1,75,000

1,51,000
No, the answer is incorrect.
Score: 0
Accepted Answers:
2,00,0002) In appreciation of the social Improvements completed in a town, a wealthy philanthropist decided to gift Rs 750 to each male senior citizen n the town and Rs 1000 to each female senior citizen, together, there were 300 senlor citizens 7 point
iil fo tis gift. Hower, oly 8/9" ofthe sible men and 2/3 ofthe ligble omen claimed the ft. Hon much money (in Rupees) dd the phiantecpist give away in tla?
150000
200000
175000
151.000
No, the answer is incorrect.
Score: 0
Accepted Answers:
200000

VIPSolutions · Accepted Answer

Let's analyze the problem step-by-step:

---

## Given Data:
- Total senior citizens: **300**
- Gift to each male senior citizen: Rs **750**
- Gift to each female senior citizen: Rs **100**
- **8/9** of eligible men claimed the gift
- **2/3** of eligible women claimed the gift
- Total amount given away: Rs **2,00,000** (accepted answer)

---

## Step 1: Let the total number of male senior citizens be $ M $
and the total number of female senior citizens be $ F $.

From the total:
$$
M + F = 300
$$

---

## Step 2: Express the number of men and women who claimed the gift:

- Men who claimed: $\frac{8}{9} M$
- Women who claimed: $\frac{2}{3} F$

---

## Step 3: Calculate the total amount given:

$$
\text{Total} = \left(\frac{8}{9} M \times 750\right) + \left(\frac{2}{3} F \times 100\right)
$$

---

## Step 4: Simplify the amounts:

$$
\text{Total} = \left(\frac{8}{9} M \times 750\right) + \left(\frac{2}{3} F \times 100\right)
$$

Calculations:

$$
\frac{8}{9} M \times 750 = \frac{8 \times 750}{9} M = \frac{600}{9} M = \frac{200}{3} M
$$

$$
\frac{2}{3} F \times 100 = \frac{2 \times 100}{3} F = \frac{200}{3} F
$$

Total:

$$
\text{Total} = \frac{200}{3} M + \frac{200}{3} F = \frac{200}{3} (M + F)
$$

Since $ M + F = 300 $:

$$
\text{Total} = \frac{200}{3} \times 300
$$

$$
= 200 \times 100 = 200,000
$$

---

## **Final Answer:**

$$
\boxed{\text{Rs 2,00,000}}
$$

This matches the accepted answer.

---

## **Summary:**
The total money given away is Rs **2,00,000**.

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